Nonsmooth Differential Geometry An Approach Tailored For Spaces With Ricci Curvature Bounded From Below
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Nonsmooth Differential Geometry
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Author : Nicola Gigli
language : en
Publisher:
Release Date : 2018
Nonsmooth Differential Geometry written by Nicola Gigli and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Geometry, Differential categories.
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.
Lectures On Nonsmooth Differential Geometry
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Author : Nicola Gigli
language : en
Publisher: Springer Nature
Release Date : 2020-02-10
Lectures On Nonsmooth Differential Geometry written by Nicola Gigli and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-10 with Mathematics categories.
This book provides an introduction to some aspects of the flourishing field of nonsmooth geometric analysis. In particular, a quite detailed account of the first-order structure of general metric measure spaces is presented, and the reader is introduced to the second-order calculus on spaces – known as RCD spaces – satisfying a synthetic lower Ricci curvature bound. Examples of the main topics covered include notions of Sobolev space on abstract metric measure spaces; normed modules, which constitute a convenient technical tool for the introduction of a robust differential structure in the nonsmooth setting; first-order differential operators and the corresponding functional spaces; the theory of heat flow and its regularizing properties, within the general framework of “infinitesimally Hilbertian” metric measure spaces; the RCD condition and its effects on the behavior of heat flow; and second-order calculus on RCD spaces. The book is mainly intended for young researchers seeking a comprehensive and fairly self-contained introduction to this active research field. The only prerequisites are a basic knowledge of functional analysis, measure theory, and Riemannian geometry.
Recent Advances In Alexandrov Geometry
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Author : Gerardo Arizmendi Echegaray
language : en
Publisher: Springer Nature
Release Date : 2022-10-27
Recent Advances In Alexandrov Geometry written by Gerardo Arizmendi Echegaray and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-27 with Mathematics categories.
This volume is devoted to various aspects of Alexandrov Geometry for those wishing to get a detailed picture of the advances in the field. It contains enhanced versions of the lecture notes of the two mini-courses plus those of one research talk given at CIMAT. Peter Petersen’s part aims at presenting various rigidity results about Alexandrov spaces in a way that facilitates the understanding by a larger audience of geometers of some of the current research in the subject. They contain a brief overview of the fundamental aspects of the theory of Alexandrov spaces with lower curvature bounds, as well as the aforementioned rigidity results with complete proofs. The text from Fernando Galaz-García’s minicourse was completed in collaboration with Jesús Nuñez-Zimbrón. It presents an up-to-date and panoramic view of the topology and geometry of 3-dimensional Alexandrov spaces, including the classification of positively and non-negatively curved spaces and the geometrization theorem. They also present Lie group actions and their topological and equivariant classifications as well as a brief account of results on collapsing Alexandrov spaces. Jesús Nuñez-Zimbrón’s contribution surveys two recent developments in the understanding of the topological and geometric rigidity of singular spaces with curvature bounded below.
Vector Calculus For Tamed Dirichlet Spaces
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Author : Mathias Braun
language : en
Publisher: American Mathematical Society
Release Date : 2025-01-08
Vector Calculus For Tamed Dirichlet Spaces written by Mathias Braun 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 2025-01-08 with Mathematics categories.
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Elliptic Pdes On Compact Ricci Limit Spaces And Applications
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Author : Shouhei Honda
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29
Elliptic Pdes On Compact Ricci Limit Spaces And Applications written by Shouhei Honda 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 2018-05-29 with Mathematics categories.
In this paper the author studies elliptic PDEs on compact Gromov-Hausdorff limit spaces of Riemannian manifolds with lower Ricci curvature bounds. In particular the author establishes continuities of geometric quantities, which include solutions of Poisson's equations, eigenvalues of Schrödinger operators, generalized Yamabe constants and eigenvalues of the Hodge Laplacian, with respect to the Gromov-Hausdorff topology. The author applies these to the study of second-order differential calculus on such limit spaces.
Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes
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Author : Boyan Sirakov
language : en
Publisher: World Scientific
Release Date : 2019-02-27
Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes written by Boyan Sirakov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-27 with Mathematics categories.
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
A Morse Bott Approach To Monopole Floer Homology And The Triangulation Conjecture
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Author : Francesco Lin
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-10-03
A Morse Bott Approach To Monopole Floer Homology And The Triangulation Conjecture written by Francesco Lin 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 2018-10-03 with Mathematics categories.
In the present work the author generalizes the construction of monopole Floer homology due to Kronheimer and Mrowka to the case of a gradient flow with Morse-Bott singularities. Focusing then on the special case of a three-manifold equipped equipped with a structure which is isomorphic to its conjugate, the author defines the counterpart in this context of Manolescu's recent Pin(2)-equivariant Seiberg-Witten-Floer homology. In particular, the author provides an alternative approach to his disproof of the celebrated Triangulation conjecture.
Diophantine Approximation And The Geometry Of Limit Sets In Gromov Hyperbolic Metric Spaces
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Author : Lior Fishman
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-08-09
Diophantine Approximation And The Geometry Of Limit Sets In Gromov Hyperbolic Metric Spaces written by Lior Fishman 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 2018-08-09 with Mathematics categories.
In this paper, the authors provide a complete theory of Diophantine approximation in the limit set of a group acting on a Gromov hyperbolic metric space. This summarizes and completes a long line of results by many authors, from Patterson's classic 1976 paper to more recent results of Hersonsky and Paulin (2002, 2004, 2007). The authors consider concrete examples of situations which have not been considered before. These include geometrically infinite Kleinian groups, geometrically finite Kleinian groups where the approximating point is not a fixed point of any element of the group, and groups acting on infinite-dimensional hyperbolic space. Moreover, in addition to providing much greater generality than any prior work of which the authors are aware, the results also give new insight into the nature of the connection between Diophantine approximation and the geometry of the limit set within which it takes place. Two results are also contained here which are purely geometric: a generalization of a theorem of Bishop and Jones (1997) to Gromov hyperbolic metric spaces, and a proof that the uniformly radial limit set of a group acting on a proper geodesic Gromov hyperbolic metric space has zero Patterson–Sullivan measure unless the group is quasiconvex-cocompact. The latter is an application of a Diophantine theorem.
Neckpinch Dynamics For Asymmetric Surfaces Evolving By Mean Curvature Flow
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Author : Zhou Gang
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29
Neckpinch Dynamics For Asymmetric Surfaces Evolving By Mean Curvature Flow written by Zhou Gang 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 2018-05-29 with Mathematics categories.
The authors study noncompact surfaces evolving by mean curvature flow (mcf). For an open set of initial data that are $C^3$-close to round, but without assuming rotational symmetry or positive mean curvature, the authors show that mcf solutions become singular in finite time by forming neckpinches, and they obtain detailed asymptotics of that singularity formation. The results show in a precise way that mcf solutions become asymptotically rotationally symmetric near a neckpinch singularity.