Constant Mean Curvature Surfaces In Homogeneous Manifolds

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Constant Mean Curvature Surfaces in Homogeneous Manifolds

Author : Julia Plehnert
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832532064
Total Pages : 94 pages
Book Rating : 4.8/5 (325 download)

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Book Synopsis Constant Mean Curvature Surfaces in Homogeneous Manifolds by : Julia Plehnert

Download or read book Constant Mean Curvature Surfaces in Homogeneous Manifolds written by Julia Plehnert and published by Logos Verlag Berlin GmbH. This book was released on 2012 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation new constant mean curvature surfaces in homogeneous 3-manifolds are constructed. They arise as sister surfaces of Plateau solutions. The first example, a two-parameter family of MC H surfaces in ∑(k) x R with H ∈ [0,1/2] and k + 4H2 ≤ 0, has genus 0,2 k ends and k-fold dihedral symmetry, k ≥ 2. The existence of the minimal sister follows from the construction of a mean convex domain. The projection of the domain is non-convex. The second example is an MC 1/2 surface in H2 ∈ R with k ends, genus 1 and k-fold dihedral symmetry, k ≥ 3. One has to solve two period problems in the construction. The first period guarantees that the surface has exactly one horizontal symmetry. For the second period the control of a horizontal mirror curve proves the dihedral symmetry. For H=1/2 all surfaces are Alexandrov-embedded.

Surfaces with Constant Mean Curvature

Author : Katsuei Kenmotsu
Publisher : American Mathematical Soc.
ISBN 13 : 9780821834794
Total Pages : 156 pages
Book Rating : 4.8/5 (347 download)

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Book Synopsis Surfaces with Constant Mean Curvature by : Katsuei Kenmotsu

Download or read book Surfaces with Constant Mean Curvature written by Katsuei Kenmotsu and published by American Mathematical Soc.. This book was released on 2003 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mean curvature of a surface is an extrinsic parameter measuring how the surface is curved in the three-dimensional space. A surface whose mean curvature is zero at each point is a minimal surface, and it is known that such surfaces are models for soap film. There is a rich and well-known theory of minimal surfaces. A surface whose mean curvature is constant but nonzero is obtained when we try to minimize the area of a closed surface without changing the volume it encloses. An easy example of a surface of constant mean curvature is the sphere. A nontrivial example is provided by the constant curvature torus, whose discovery in 1984 gave a powerful incentive for studying such surfaces. Later, many examples of constant mean curvature surfaces were discovered using various methods of analysis, differential geometry, and differential equations. It is now becoming clear that there is a rich theory of surfaces of constant mean curvature. In this book, the author presents numerous examples of constant mean curvature surfaces and techniques for studying them. Many finely rendered figures illustrate the results and allow the reader to visualize and better understand these beautiful objects. The book is suitable for advanced undergraduates, graduate students and research mathematicians interested in analysis and differential geometry.

Constant Mean Curvature Annuli in Homogeneous Manifolds

Author : Miroslav Vrz̆ina
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (949 download)

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Book Synopsis Constant Mean Curvature Annuli in Homogeneous Manifolds by : Miroslav Vrz̆ina

Download or read book Constant Mean Curvature Annuli in Homogeneous Manifolds written by Miroslav Vrz̆ina and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Minimal and Constant Mean Curvature Surfaces in Various Three-manifolds

Author : Jan-Olof Jörgen Berglund
Publisher :
ISBN 13 :
Total Pages : 126 pages
Book Rating : 4.:/5 (372 download)

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Book Synopsis Minimal and Constant Mean Curvature Surfaces in Various Three-manifolds by : Jan-Olof Jörgen Berglund

Download or read book Minimal and Constant Mean Curvature Surfaces in Various Three-manifolds written by Jan-Olof Jörgen Berglund and published by . This book was released on 1997 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to CMC Surfaces in the Homogeneous Spaces E(¿,t)

Author : Carlos Peñafiel
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783659642708
Total Pages : 140 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis An Introduction to CMC Surfaces in the Homogeneous Spaces E(¿,t) by : Carlos Peñafiel

Download or read book An Introduction to CMC Surfaces in the Homogeneous Spaces E(¿,t) written by Carlos Peñafiel and published by LAP Lambert Academic Publishing. This book was released on 2015-01-06 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to students as well as professors who are interested in Differential Geometry. In particular, in the study of the theory of constant mean curvature surfaces (CMC for short) immersed in the simply connected, complete, three-dimensional homogeneous spaces. The goal of this book is a breve introduction to the study of the geometric behaviour of such CMC surfaces. Also we deal with some conditions to existence and non-existence of such surfaces.

Geometry And Topology Of Submanifolds Viii

Author : Ignace Van De Woestyne
Publisher : World Scientific
ISBN 13 : 9814547514
Total Pages : 426 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Geometry And Topology Of Submanifolds Viii by : Ignace Van De Woestyne

Download or read book Geometry And Topology Of Submanifolds Viii written by Ignace Van De Woestyne and published by World Scientific. This book was released on 1996-10-25 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings consists of papers presented at the international meeting of Differential Geometry and Computer Vision held in Norway and of international meetings on Pure and Applied Differential Geometry held in Belgium. This volume is dedicated to Prof Dr Tom Willmore for his contribution to the development of the domain of differential geometry. Furthermore, it contains a survey on recent developments on affine differential geometry, including a list of publications and a problem list.

Global Differential Geometry and Global Analysis

Author : Dirk Ferus
Publisher : Springer
ISBN 13 : 354046445X
Total Pages : 289 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Global Differential Geometry and Global Analysis by : Dirk Ferus

Download or read book Global Differential Geometry and Global Analysis written by Dirk Ferus and published by Springer. This book was released on 2006-11-14 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: All papers appearing in this volume are original research articles and have not been published elsewhere. They meet the requirements that are necessary for publication in a good quality primary journal. E.Belchev, S.Hineva: On the minimal hypersurfaces of a locally symmetric manifold. -N.Blasic, N.Bokan, P.Gilkey: The spectral geometry of the Laplacian and the conformal Laplacian for manifolds with boundary. -J.Bolton, W.M.Oxbury, L.Vrancken, L.M. Woodward: Minimal immersions of RP2 into CPn. -W.Cieslak, A. Miernowski, W.Mozgawa: Isoptics of a strictly convex curve. -F.Dillen, L.Vrancken: Generalized Cayley surfaces. -A.Ferrandez, O.J.Garay, P.Lucas: On a certain class of conformally flat Euclidean hypersurfaces. -P.Gauduchon: Self-dual manifolds with non-negative Ricci operator. -B.Hajduk: On the obstruction group toexistence of Riemannian metrics of positive scalar curvature. -U.Hammenstaedt: Compact manifolds with 1/4-pinched negative curvature. -J.Jost, Xiaowei Peng: The geometry of moduli spaces of stable vector bundles over Riemannian surfaces. - O.Kowalski, F.Tricerri: A canonical connection for locally homogeneous Riemannian manifolds. -M.Kozlowski: Some improper affine spheres in A3. -R.Kusner: A maximum principle at infinity and the topology of complete embedded surfaces with constant mean curvature. -Anmin Li: Affine completeness and Euclidean completeness. -U.Lumiste: On submanifolds with parallel higher order fundamental form in Euclidean spaces. -A.Martinez, F.Milan: Convex affine surfaces with constant affine mean curvature. -M.Min-Oo, E.A.Ruh, P.Tondeur: Transversal curvature and tautness for Riemannian foliations. -S.Montiel, A.Ros: Schroedinger operators associated to a holomorphic map. -D.Motreanu: Generic existence of Morse functions on infinite dimensional Riemannian manifolds and applications. -B.Opozda: Some extensions of Radon's theorem.

Surfaces in Constant Curvature Manifolds with Parallel Mean Curvature Vector Field

Author : David A. Hoffman
Publisher :
ISBN 13 :
Total Pages : 140 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Surfaces in Constant Curvature Manifolds with Parallel Mean Curvature Vector Field by : David A. Hoffman

Download or read book Surfaces in Constant Curvature Manifolds with Parallel Mean Curvature Vector Field written by David A. Hoffman and published by . This book was released on 1971 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author :
Publisher : World Scientific
ISBN 13 :
Total Pages : 1191 pages
Book Rating : 4./5 ( download)

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Book Synopsis by :

Download or read book written by and published by World Scientific. This book was released on with total page 1191 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The CMC Dynamics Theorem in R^3

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (632 download)

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Book Synopsis The CMC Dynamics Theorem in R^3 by :

Download or read book The CMC Dynamics Theorem in R^3 written by and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we develop some new tools and theory that are useful in describing the geometry of properly embedded, constant mean curvature surfaces in R^3 with bounded second fundamental form. More precisely, we prove dynamics type results for the space of translational limits of such a surface. As a consequence of our main theorems, in subsequent papers we obtain rigidity results for certain properly embedded, constant mean curvature surfaces in R^3, as well as derive curvature estimates for complete, embedded, constant mean curvature surfaces in complete locally homogeneous three- manifolds.

Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition

Author :
Publisher : ScholarlyEditions
ISBN 13 : 1464964793
Total Pages : 995 pages
Book Rating : 4.4/5 (649 download)

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Book Synopsis Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition by :

Download or read book Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition written by and published by ScholarlyEditions. This book was released on 2012-01-09 with total page 995 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Logic, Operations, and Computational Mathematics and Geometry. The editors have built Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Logic, Operations, and Computational Mathematics and Geometry in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Prescribing the Curvature of a Riemannian Manifold

Author : Jerry L. Kazdan
Publisher : American Mathematical Soc.
ISBN 13 : 9780821889022
Total Pages : 68 pages
Book Rating : 4.8/5 (89 download)

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Book Synopsis Prescribing the Curvature of a Riemannian Manifold by : Jerry L. Kazdan

Download or read book Prescribing the Curvature of a Riemannian Manifold written by Jerry L. Kazdan and published by American Mathematical Soc.. This book was released on 1985-12-31 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes were the basis for a series of ten lectures given in January 1984 at Polytechnic Institute of New York under the sponsorship of the Conference Board of the Mathematical Sciences and the National Science Foundation. The lectures were aimed at mathematicians who knew either some differential geometry or partial differential equations, although others could understand the lectures. Author's Summary:Given a Riemannian Manifold $(M,g)$ one can compute the sectional, Ricci, and scalar curvatures. In other special circumstances one also has mean curvatures, holomorphic curvatures, etc. The inverse problem is, given a candidate for some curvature, to determine if there is some metric $g$ with that as its curvature. One may also restrict ones attention to a special class of metrics, such as Kahler or conformal metrics, or those coming from an embedding. These problems lead one to (try to) solve nonlinear partial differential equations. However, there may be topological or analytic obstructions to solving these equations. A discussion of these problems thus requires a balanced understanding between various existence and non-existence results. The intent of this volume is to give an up-to-date survey of these questions, including enough background, so that the current research literature is accessible to mathematicians who are not necessarily experts in PDE or differential geometry. The intended audience is mathematicians and graduate students who know either PDE or differential geometry at roughly the level of an intermediate graduate course.

Geometric Analysis

Author : Joaqun Prez
Publisher : American Mathematical Soc.
ISBN 13 : 0821849921
Total Pages : 198 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometric Analysis by : Joaqun Prez

Download or read book Geometric Analysis written by Joaqun Prez and published by American Mathematical Soc.. This book was released on 2012-07-16 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains research and expository articles from the courses and talks given at the RSME Lluis A. Santalo Summer School, ``Geometric Analysis'', held June 28-July 2, 2010, in Granada, Spain. The goal of the Summer School was to present some of the many advances currently taking place in the interaction between partial differential equations and differential geometry, with special emphasis on the theory of minimal surfaces. This volume includes expository articles about the current state of specific problems involving curvature and partial differential equations, with interactions to neighboring fields such as probability. An introductory, mostly self-contained course on constant mean curvature surfaces in Lie groups equipped with a left invariant metric is provided. The volume will be of interest to researchers, post-docs, and advanced PhD students in the interface between partial differential equations and differential geometry.

Isoperimetric Inequalities in Riemannian Manifolds

Author : Manuel Ritoré
Publisher : Springer Nature
ISBN 13 : 3031379012
Total Pages : 470 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Isoperimetric Inequalities in Riemannian Manifolds by : Manuel Ritoré

Download or read book Isoperimetric Inequalities in Riemannian Manifolds written by Manuel Ritoré and published by Springer Nature. This book was released on 2023-10-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work gives a coherent introduction to isoperimetric inequalities in Riemannian manifolds, featuring many of the results obtained during the last 25 years and discussing different techniques in the area. Written in a clear and appealing style, the book includes sufficient introductory material, making it also accessible to graduate students. It will be of interest to researchers working on geometric inequalities either from a geometric or analytic point of view, but also to those interested in applying the described techniques to their field.

Constant Mean Curvature Surfaces with Boundary

Author : Rafael López
Publisher : Springer Science & Business Media
ISBN 13 : 3642396267
Total Pages : 296 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Constant Mean Curvature Surfaces with Boundary by : Rafael López

Download or read book Constant Mean Curvature Surfaces with Boundary written by Rafael López and published by Springer Science & Business Media. This book was released on 2013-08-31 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of surfaces with constant mean curvature (CMC) is one of the main topics in classical differential geometry. Moreover, CMC surfaces are important mathematical models for the physics of interfaces in the absence of gravity, where they separate two different media or for capillary phenomena. Further, as most techniques used in the theory of CMC surfaces not only involve geometric methods but also PDE and complex analysis, the theory is also of great interest for many other mathematical fields. While minimal surfaces and CMC surfaces in general have already been treated in the literature, the present work is the first to present a comprehensive study of “compact surfaces with boundaries,” narrowing its focus to a geometric view. Basic issues include the discussion whether the symmetries of the curve inherit to the surface; the possible values of the mean curvature, area and volume; stability; the circular boundary case and the existence of the Plateau problem in the non-parametric case. The exposition provides an outlook on recent research but also a set of techniques that allows the results to be expanded to other ambient spaces. Throughout the text, numerous illustrations clarify the results and their proofs. The book is intended for graduate students and researchers in the field of differential geometry and especially theory of surfaces, including geometric analysis and geometric PDEs. It guides readers up to the state-of-the-art of the theory and introduces them to interesting open problems.

New Trends in Geometric Analysis

Author : Antonio Alarcón
Publisher : Springer Nature
ISBN 13 : 3031399161
Total Pages : 398 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis New Trends in Geometric Analysis by : Antonio Alarcón

Download or read book New Trends in Geometric Analysis written by Antonio Alarcón and published by Springer Nature. This book was released on 2023-11-25 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide an overview of some of the progress made by the Spanish Network of Geometric Analysis (REAG, by its Spanish acronym) since its born in 2007. REAG was created with the objective of enabling the interchange of ideas and the knowledge transfer between several Spanish groups having Geometric Analysis as a common research line. This includes nine groups at Universidad Autónoma de Barcelona, Universidad Autónoma de Madrid, Universidad de Granada, Universidad Jaume I de Castellón, Universidad de Murcia, Universidad de Santiago de Compostela and Universidad de Valencia. The success of REAG has been substantiated with regular meetings and the publication of research papers obtained in collaboration between the members of different nodes. On the occasion of the 15th anniversary of REAG this book aims to collect some old and new contributions of this network to Geometric Analysis. The book consists of thirteen independent chapters, all of them authored by current members of REAG. The topics under study cover geometric flows, constant mean curvature surfaces in Riemannian and sub-Riemannian spaces, integral geometry, potential theory and Riemannian geometry, among others. Some of these chapters have been written in collaboration between members of different nodes of the network, and show the fruitfulness of the common research atmosphere provided by REAG. The rest of the chapters survey a research line or present recent progresses within a group of those forming REAG. Surveying several research lines and offering new directions in the field, the volume is addressed to researchers (including postdocs and PhD students) in Geometric Analysis in the large.

Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures

Download Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures PDF Online Free

Author : Rajendra Bhatia
Publisher : World Scientific
ISBN 13 : 9814462934
Total Pages : 4137 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures by : Rajendra Bhatia

Download or read book Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures written by Rajendra Bhatia and published by World Scientific. This book was released on 2011-06-06 with total page 4137 pages. Available in PDF, EPUB and Kindle. Book excerpt: ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.