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Weakly Differentiable Mappings Between Manifolds
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Book Synopsis Weakly Differentiable Mappings between Manifolds by : Piotr Hajłasz
Download or read book Weakly Differentiable Mappings between Manifolds written by Piotr Hajłasz and published by American Mathematical Soc.. This book was released on 2008 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study Sobolev classes of weakly differentiable mappings $f: {\mathbb X}\rightarrow {\mathbb Y}$ between compact Riemannian manifolds without boundary. These mappings need not be continuous. They actually possess less regularity than the mappings in ${\mathcal W}{1, n}({\mathbb X}\, \, {\mathbb Y})\, $, $n=\mbox{dim}\, {\mathbb X}$. The central themes being discussed a
Book Synopsis Weakly Differentiable Mappings Between Manifolds by : P. Hajlasz
Download or read book Weakly Differentiable Mappings Between Manifolds written by P. Hajlasz and published by . This book was released on 2004 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Weakly Differentiable Mappings Between Manifolds by :
Download or read book Weakly Differentiable Mappings Between Manifolds written by and published by American Mathematical Soc.. This book was released on 2008-02-15 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study Sobolev classes of weakly differentiable mappings $f:{\mathbb X}\rightarrow {\mathbb Y}$ between compact Riemannian manifolds without boundary. These mappings need not be continuous. They actually possess less regularity than the mappings in ${\mathcal W}^{1,n}({\mathbb X}\, ,\, {\mathbb Y})\,$, $n=\mbox{dim}\, {\mathbb X}$. The central themes being discussed are: smooth approximation of those mappings integrability of the Jacobian determinant The approximation problem in the category of Sobolev spaces between manifolds ${\mathcal W}^{1,p}({\mathbb X}\, ,\, {\mathbb Y})$, $1\leqslant p \leqslant n$, has been recently settled. However, the point of the results is that the authors make no topological restrictions on manifolds ${\mathbb X}$ and ${\mathbb Y}$. They characterize, essentially all, classes of weakly differentiable mappings which satisfy the approximation property. The novelty of their approach is that they were able to detect tiny sets on which the mappings are continuous. These sets give rise to the so-called web-like structure of ${\mathbb X}$ associated with the given mapping $f: {\mathbb X}\rightarrow {\mathbb Y}$. The integrability theory of Jacobians in a manifold setting is really different than one might a priori expect based on the results in the Euclidean space. To the authors' surprise, the case when the target manifold ${\mathbb Y}$ admits only trivial cohomology groups $H^\ell ({\mathbb Y})$, $1\leqslant \ell
Book Synopsis The Mapping Class Group from the Viewpoint of Measure Equivalence Theory by : Yoshikata Kida
Download or read book The Mapping Class Group from the Viewpoint of Measure Equivalence Theory written by Yoshikata Kida and published by American Mathematical Soc.. This book was released on 2008 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author obtains some classification result for the mapping class groups of compact orientable surfaces in terms of measure equivalence. In particular, the mapping class groups of different closed surfaces cannot be measure equivalent. Moreover, the author gives various examples of discrete groups which are not measure equivalent to the mapping class groups. In the course of the proof, the author investigates amenability in a measurable sense for the actions of the mapping class group on the boundary at infinity of the curve complex and on the Thurston boundary and, using this investigation, proves that the mapping class group of a compact orientable surface is exact.
Book Synopsis Handbook of Global Analysis by : Demeter Krupka
Download or read book Handbook of Global Analysis written by Demeter Krupka and published by Elsevier. This book was released on 2011-08-11 with total page 1243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics.This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics- Written by world-experts in the field- Up-to-date contents
Book Synopsis The Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations by : Salah-Eldin Mohammed
Download or read book The Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations written by Salah-Eldin Mohammed and published by American Mathematical Soc.. This book was released on 2008 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of this paper is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations and stochastic partial differential equations near stationary solutions.
Book Synopsis Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models by : Pierre Magal
Download or read book Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models written by Pierre Magal and published by American Mathematical Soc.. This book was released on 2009 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several types of differential equations, such as delay differential equations, age-structure models in population dynamics, evolution equations with boundary conditions, can be written as semilinear Cauchy problems with an operator which is not densely defined in its domain. The goal of this paper is to develop a center manifold theory for semilinear Cauchy problems with non-dense domain. Using Liapunov-Perron method and following the techniques of Vanderbauwhede et al. in treating infinite dimensional systems, the authors study the existence and smoothness of center manifolds for semilinear Cauchy problems with non-dense domain. As an application, they use the center manifold theorem to establish a Hopf bifurcation theorem for age structured models.
Book Synopsis Topology of Singular Fibers of Differentiable Maps by : Osamu Saeki
Download or read book Topology of Singular Fibers of Differentiable Maps written by Osamu Saeki and published by Springer Science & Business Media. This book was released on 2004 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Toroidal Dehn Fillings on Hyperbolic 3-Manifolds by : Cameron Gordon
Download or read book Toroidal Dehn Fillings on Hyperbolic 3-Manifolds written by Cameron Gordon and published by American Mathematical Soc.. This book was released on 2008 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors determine all hyperbolic $3$-manifolds $M$ admitting two toroidal Dehn fillings at distance $4$ or $5$. They show that if $M$ is a hyperbolic $3$-manifold with a torus boundary component $T 0$, and $r,s$ are two slopes on $T 0$ with $\Delta(r,s) = 4$ or $5$ such that $M(r)$ and $M(s)$ both contain an essential torus, then $M$ is either one of $14$ specific manifolds $M i$, or obtained from $M 1, M 2, M 3$ or $M {14}$ by attaching a solid torus to $\partial M i - T 0$.All the manifolds $M i$ are hyperbolic, and the authors show that only the first three can be embedded into $S3$. As a consequence, this leads to a complete classification of all hyperbolic knots in $S3$ admitting two toroidal surgeries with distance at least $4$.
Book Synopsis Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds by : Raphael Ponge
Download or read book Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds written by Raphael Ponge and published by American Mathematical Soc.. This book was released on 2008 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir deals with the hypoelliptic calculus on Heisenberg manifolds, including CR and contact manifolds. In this context the main differential operators at stake include the Hormander's sum of squares, the Kohn Laplacian, the horizontal sublaplacian, the CR conformal operators of Gover-Graham and the contact Laplacian. These operators cannot be elliptic and the relevant pseudodifferential calculus to study them is provided by the Heisenberg calculus of Beals-Greiner andTaylor.
Book Synopsis The Interaction of Analysis and Geometry by : Victor I. Burenkov
Download or read book The Interaction of Analysis and Geometry written by Victor I. Burenkov and published by American Mathematical Soc.. This book was released on 2007 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on talks given at the International Conference on Analysis and Geometry in honor of the 75th birthday of Yurii Reshetnyak (Novosibirsk, 2004), this title includes topics such as geometry of spaces with bounded curvature in the sense of Alexandrov, quasiconformal mappings and mappings with bounded distortion, and nonlinear potential theory."
Book Synopsis On the convergence of $\sum c_kf(n_kx)$ by : Istvan Berkes
Download or read book On the convergence of $\sum c_kf(n_kx)$ written by Istvan Berkes and published by American Mathematical Soc.. This book was released on 2009 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a general study of the convergence problem and intends to prove several fresh results and improve a number of old results in the field. This title studies the case when the nk are random and investigates the discrepancy the sequence (nkx) mod 1.
Book Synopsis Degree Theory for Operators of Monotone Type and Nonlinear Elliptic Equations with Inequality Constraints by : Sergiu Aizicovici
Download or read book Degree Theory for Operators of Monotone Type and Nonlinear Elliptic Equations with Inequality Constraints written by Sergiu Aizicovici and published by American Mathematical Soc.. This book was released on 2008 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors examine the degree map of multivalued perturbations of nonlinear operators of monotone type and prove that at a local minimizer of the corresponding Euler functional, this degree equals one.
Book Synopsis Noncommutative Curves of Genus Zero by : Dirk Kussin
Download or read book Noncommutative Curves of Genus Zero written by Dirk Kussin and published by American Mathematical Soc.. This book was released on 2009-08-07 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these notes the author investigates noncommutative smooth projective curves of genus zero, also called exceptional curves. As a main result he shows that each such curve $\mathbb{X}$ admits, up to some weighting, a projective coordinate algebra which is a not necessarily commutative graded factorial domain $R$ in the sense of Chatters and Jordan. Moreover, there is a natural bijection between the points of $\mathbb{X}$ and the homogeneous prime ideals of height one in $R$, and these prime ideals are principal in a strong sense.
Book Synopsis The Creation of Strange Non-Chaotic Attractors in Non-Smooth Saddle-Node Bifurcations by : Tobias H. Jger
Download or read book The Creation of Strange Non-Chaotic Attractors in Non-Smooth Saddle-Node Bifurcations written by Tobias H. Jger and published by American Mathematical Soc.. This book was released on 2009-08-07 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author proposes a general mechanism by which strange non-chaotic attractors (SNA) are created during the collision of invariant curves in quasiperiodically forced systems. This mechanism, and its implementation in different models, is first discussed on an heuristic level and by means of simulations. In the considered examples, a stable and an unstable invariant circle undergo a saddle-node bifurcation, but instead of a neutral invariant curve there exists a strange non-chaotic attractor-repeller pair at the bifurcation point. This process is accompanied by a very characteristic behaviour of the invariant curves prior to their collision, which the author calls `exponential evolution of peaks'.
Book Synopsis Representations of Shifted Yangians and Finite $W$-algebras by : Jonathan Brundan
Download or read book Representations of Shifted Yangians and Finite $W$-algebras written by Jonathan Brundan and published by American Mathematical Soc.. This book was released on 2008 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study highest weight representations of shifted Yangians over an algebraically closed field of characteristic $0$. In particular, they classify the finite dimensional irreducible representations and explain how to compute their Gelfand-Tsetlin characters in terms of known characters of standard modules and certain Kazhdan-Lusztig polynomials. The authors' approach exploits the relationship between shifted Yangians and the finite W-algebras associated to nilpotent orbits in general linear Lie algebras.
Book Synopsis Large Deviations and Adiabatic Transitions for Dynamical Systems and Markov Processes in Fully Coupled Averaging by : Yuri Kifer
Download or read book Large Deviations and Adiabatic Transitions for Dynamical Systems and Markov Processes in Fully Coupled Averaging written by Yuri Kifer and published by American Mathematical Soc.. This book was released on 2009-08-07 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The work treats dynamical systems given by ordinary differential equations in the form $\frac{dX^\varepsilon(t)}{dt}=\varepsilon B(X^\varepsilon(t),Y^\varepsilon(t))$ where fast motions $Y^\varepsilon$ depend on the slow motion $X^\varepsilon$ (coupled with it) and they are either given by another differential equation $\frac{dY^\varepsilon(t)}{dt}=b(X^\varepsilon(t), Y^\varepsilon(t))$ or perturbations of an appropriate parametric family of Markov processes with freezed slow variables.
