The Space Of Spaces Curvature Bounds And Gradient Flows On The Space Of Metric Measure Spaces
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The Space Of Spaces Curvature Bounds And Gradient Flows On The Space Of Metric Measure Spaces
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Author : Karl-Theodor Sturm
language : en
Publisher: American Mathematical Society
Release Date : 2023-11-27
The Space Of Spaces Curvature Bounds And Gradient Flows On The Space Of Metric Measure Spaces written by Karl-Theodor Sturm and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-27 with Mathematics categories.
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Alexandrov Geometry
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Author : Stephanie Alexander
language : en
Publisher: American Mathematical Society
Release Date : 2024-05-24
Alexandrov Geometry written by Stephanie Alexander and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-24 with Mathematics categories.
Alexandrov spaces are defined via axioms similar to those of the Euclid axioms but where certain equalities are replaced with inequalities. Depending on the signs of the inequalities, we obtain Alexandrov spaces with curvature bounded above (CBA) and curvature bounded below (CBB). Even though the definitions of the two classes of spaces are similar, their properties and known applications are quite different. The goal of this book is to give a comprehensive exposition of the structure theory of Alexandrov spaces with curvature bounded above and below. It includes all the basic material as well as selected topics inspired by considering Alexandrov spaces with CBA and with CBB simultaneously. The book also includes an extensive problem list with solutions indicated for every problem.
Nonlinear Diffusion Equations And Curvature Conditions In Metric Measure Spaces
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Author : Luigi Ambrosio
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-02-13
Nonlinear Diffusion Equations And Curvature Conditions In Metric Measure Spaces written by Luigi Ambrosio and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-13 with Education categories.
The aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces (X,d,m). On the geometric side, the authors' new approach takes into account suitable weighted action functionals which provide the natural modulus of K-convexity when one investigates the convexity properties of N-dimensional entropies. On the side of diffusion semigroups and evolution variational inequalities, the authors' new approach uses the nonlinear diffusion semigroup induced by the N-dimensional entropy, in place of the heat flow. Under suitable assumptions (most notably the quadraticity of Cheeger's energy relative to the metric measure structure) both approaches are shown to be equivalent to the strong CD∗(K,N) condition of Bacher-Sturm.
Modern Approaches To Discrete Curvature
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Author : Laurent Najman
language : en
Publisher: Springer
Release Date : 2017-10-04
Modern Approaches To Discrete Curvature written by Laurent Najman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-04 with Mathematics categories.
This book provides a valuable glimpse into discrete curvature, a rich new field of research which blends discrete mathematics, differential geometry, probability and computer graphics. It includes a vast collection of ideas and tools which will offer something new to all interested readers. Discrete geometry has arisen as much as a theoretical development as in response to unforeseen challenges coming from applications. Discrete and continuous geometries have turned out to be intimately connected. Discrete curvature is the key concept connecting them through many bridges in numerous fields: metric spaces, Riemannian and Euclidean geometries, geometric measure theory, topology, partial differential equations, calculus of variations, gradient flows, asymptotic analysis, probability, harmonic analysis, graph theory, etc. In spite of its crucial importance both in theoretical mathematics and in applications, up to now, almost no books have provided a coherent outlook on this emerging field.
Nonsmooth Differential Geometry An Approach Tailored For Spaces With Ricci Curvature Bounded From Below
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Author : Nicola Gigli
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-02-23
Nonsmooth Differential Geometry An Approach Tailored For Spaces With Ricci Curvature Bounded From Below written by Nicola Gigli and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-23 with Mathematics categories.
The author discusses in which sense general metric measure spaces possess a first order differential structure. Building on this, spaces with Ricci curvature bounded from below a second order calculus can be developed, permitting the author to define Hessian, covariant/exterior derivatives and Ricci curvature.
Eulerian Spaces
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Author : Paul Gartside
language : en
Publisher: American Mathematical Society
Release Date : 2024-01-26
Eulerian Spaces written by Paul Gartside and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-26 with Mathematics categories.
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Empirical Measures Geodesic Lengths And A Variational Formula In First Passage Percolation
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Author : Erik Bates
language : en
Publisher: American Mathematical Society
Release Date : 2024-02-01
Empirical Measures Geodesic Lengths And A Variational Formula In First Passage Percolation written by Erik Bates and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-01 with Mathematics categories.
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New Trends On Analysis And Geometry In Metric Spaces
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Author : Fabrice Baudoin
language : en
Publisher: Springer Nature
Release Date : 2022-02-04
New Trends On Analysis And Geometry In Metric Spaces written by Fabrice Baudoin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-04 with Mathematics categories.
This book includes four courses on geometric measure theory, the calculus of variations, partial differential equations, and differential geometry. Authored by leading experts in their fields, the lectures present different approaches to research topics with the common background of a relevant underlying, usually non-Riemannian, geometric structure. In particular, the topics covered concern differentiation and functions of bounded variation in metric spaces, Sobolev spaces, and differential geometry in the so-called Carnot–Carathéodory spaces. The text is based on lectures presented at the 10th School on "Analysis and Geometry in Metric Spaces" held in Levico Terme (TN), Italy, in collaboration with the University of Trento, Fondazione Bruno Kessler and CIME, Italy. The book is addressed to both graduate students and researchers.
Gradient Flows
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Author : Luigi Ambrosio
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-29
Gradient Flows written by Luigi Ambrosio and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-29 with Mathematics categories.
The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.
Quasi Periodic Traveling Waves On An Infinitely Deep Perfect Fluid Under Gravity
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Author : Roberto Feola
language : en
Publisher: American Mathematical Society
Release Date : 2024-04-17
Quasi Periodic Traveling Waves On An Infinitely Deep Perfect Fluid Under Gravity written by Roberto Feola and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-17 with Mathematics categories.
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