Needle Decompositions In Riemannian Geometry

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Needle Decompositions In Riemannian Geometry

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Author : Bo’az Klartag
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-09-25

Needle Decompositions In Riemannian Geometry written by Bo’az Klartag 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 2017-09-25 with Curvature categories.

The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.

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 Geometry, Differential 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.

On Sudakov S Type Decomposition Of Transference Plans With Norm Costs

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Author : Stefano Bianchini
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-02-23

On Sudakov S Type Decomposition Of Transference Plans With Norm Costs written by Stefano Bianchini 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 Decomposition (Mathematics) categories.

The authors consider the original strategy proposed by Sudakov for solving the Monge transportation problem with norm cost with , probability measures in and absolutely continuous w.r.t. . The key idea in this approach is to decompose (via disintegration of measures) the Kantorovich optimal transportation problem into a family of transportation problems in , where are disjoint regions such that the construction of an optimal map is simpler than in the original problem, and then to obtain by piecing together the maps . When the norm is strictly convex, the sets are a family of -dimensional segments determined by the Kantorovich potential called optimal rays, while the existence of the map is straightforward provided one can show that the disintegration of (and thus of ) on such segments is absolutely continuous w.r.t. the -dimensional Hausdorff measure. When the norm is not strictly convex, the main problems in this kind of approach are two: first, to identify a suitable family of regions on which the transport problem decomposes into simpler ones, and then to prove the existence of optimal maps. In this paper the authors show how these difficulties can be overcome, and that the original idea of Sudakov can be successfully implemented. The results yield a complete characterization of the Kantorovich optimal transportation problem, whose straightforward corollary is the solution of the Monge problem in each set and then in . The strategy is sufficiently powerful to be applied to other optimal transportation problems.

Comparison Finsler Geometry

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Author : Shin-ichi Ohta
language : en
Publisher: Springer Nature
Release Date : 2021-10-09

Comparison Finsler Geometry written by Shin-ichi Ohta and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-09 with Mathematics categories.

This monograph presents recent developments in comparison geometry and geometric analysis on Finsler manifolds. Generalizing the weighted Ricci curvature into the Finsler setting, the author systematically derives the fundamental geometric and analytic inequalities in the Finsler context. Relying only upon knowledge of differentiable manifolds, this treatment offers an accessible entry point to Finsler geometry for readers new to the area. Divided into three parts, the book begins by establishing the fundamentals of Finsler geometry, including Jacobi fields and curvature tensors, variation formulas for arc length, and some classical comparison theorems. Part II goes on to introduce the weighted Ricci curvature, nonlinear Laplacian, and nonlinear heat flow on Finsler manifolds. These tools allow the derivation of the Bochner–Weitzenböck formula and the corresponding Bochner inequality, gradient estimates, Bakry–Ledoux’s Gaussian isoperimetric inequality, and functional inequalities in the Finsler setting. Part III comprises advanced topics: a generalization of the classical Cheeger–Gromoll splitting theorem, the curvature-dimension condition, and the needle decomposition. Throughout, geometric descriptions illuminate the intuition behind the results, while exercises provide opportunities for active engagement. Comparison Finsler Geometry offers an ideal gateway to the study of Finsler manifolds for graduate students and researchers. Knowledge of differentiable manifold theory is assumed, along with the fundamentals of functional analysis. Familiarity with Riemannian geometry is not required, though readers with a background in the area will find their insights are readily transferrable.

Szeg Kernel Asymptotics For High Power Of Cr Line Bundles And Kodaira Embedding Theorems On Cr Manifolds

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Author : Chin-Yu Hsiao
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-08-09

Szeg Kernel Asymptotics For High Power Of Cr Line Bundles And Kodaira Embedding Theorems On Cr Manifolds written by Chin-Yu Hsiao 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 categories.

Let X be an abstract not necessarily compact orientable CR manifold of dimension 2n−1, n⩾2, and let Lk be the k-th tensor power of a CR complex line bundle L over X. Given q∈{0,1,…,n−1}, let □(q)b,k be the Gaffney extension of Kohn Laplacian for (0,q) forms with values in Lk. For λ≥0, let Π(q)k,≤λ:=E((−∞,λ]), where E denotes the spectral measure of □(q)b,k. In this work, the author proves that Π(q)k,≤k−N0F∗k, FkΠ(q)k,≤k−N0F∗k, N0≥1, admit asymptotic expansions with respect to k on the non-degenerate part of the characteristic manifold of □(q)b,k, where Fk is some kind of microlocal cut-off function. Moreover, we show that FkΠ(q)k,≤0F∗k admits a full asymptotic expansion with respect to k if □(q)b,k has small spectral gap property with respect to Fk and Π(q)k,≤0 is k-negligible away the diagonal with respect to Fk. By using these asymptotics, the authors establish almost Kodaira embedding theorems on CR manifolds and Kodaira embedding theorems on CR manifolds with transversal CR S1 action.

On Non Generic Finite Subgroups Of Exceptional Algebraic Groups

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Author : Alastair J. Litterick
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29

On Non Generic Finite Subgroups Of Exceptional Algebraic Groups written by Alastair J. Litterick 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 Affine algebraic groups categories.

Holomorphic Automorphic Forms And Cohomology

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Author : Roelof Bruggeman
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29

Holomorphic Automorphic Forms And Cohomology written by Roelof Bruggeman 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 Algebraic topology categories.

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 Geometry, Differential 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.

Mathematical Study Of Degenerate Boundary Layers A Large Scale Ocean Circulation Problem

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Author : Anne-Laure Dalibard
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29

Mathematical Study Of Degenerate Boundary Layers A Large Scale Ocean Circulation Problem written by Anne-Laure Dalibard 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 Boundary layer categories.

Globally Generated Vector Bundles With Small C1 On Projective Spaces

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Author : Cristian Anghel
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29

Globally Generated Vector Bundles With Small C1 On Projective Spaces written by Cristian Anghel 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 Chern classes categories.