Minimality And Stability Properties In Sobolev And Isoperimetric Inequalities
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Author |
: Robin Tonra Neumayer |
Publisher |
: |
Total Pages |
: 400 |
Release |
: 2017 |
ISBN-10 |
: OCLC:1023039336 |
ISBN-13 |
: |
Rating |
: 4/5 (36 Downloads) |
Synopsis Minimality and Stability Properties in Sobolev and Isoperimetric Inequalities by : Robin Tonra Neumayer
This thesis addresses the characterization of minimizers in various Sobolev- and isoperimetric-type inequalities and the analysis of the corresponding stability phenomena. We first investigate a family of variational problems which arise in connection to a suitable interpolation between the classical Sobolev and Sobolev trace inequalities. We provide a full characterization of minimizers for each problem, in turn deriving a new family of sharp constrained Sobolev inequalities on the half-space. We then prove novel stability results for the Sobolev inequality and for the anisotropic isoperimetric inequality. Both of these results share the feature of being “strong-form” stability results, in the sense that the deficit in the inequality is shown to control the strongest possible distance to the family of equality cases.
Author |
: Manuel Ritoré |
Publisher |
: Springer Nature |
Total Pages |
: 470 |
Release |
: 2023-10-06 |
ISBN-10 |
: 9783031379017 |
ISBN-13 |
: 3031379012 |
Rating |
: 4/5 (17 Downloads) |
Synopsis Isoperimetric Inequalities in Riemannian Manifolds by : Manuel Ritoré
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.
Author |
: W.-Y. Hsiang |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 258 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461381099 |
ISBN-13 |
: 1461381096 |
Rating |
: 4/5 (99 Downloads) |
Synopsis The Chern Symposium 1979 by : W.-Y. Hsiang
This volume attests to the vitality of differential geometry as it probes deeper into its internal structure and explores ever widening connections with other subjects in mathematics and physics. To most of us Professor S. S. Chern is modern differential geometry, and we, his students, are grateful to him for leading us to this fertile landscape. The aims of the symposium were to review recent developments in geometry and to expose and explore new areas of research. It was our way of honoring Professor Chern upon the occasion of his official retirement as Professor of Mathematics at the University of California. This book is a record of the scientific events of the symposium and reflects Professor Chern's wide interest and influence. The conference also reflected Professor Chern's personality. It was a serious occasion, active yet relaxed, mixed with gentleness and good humor. We wish him good health, a long life, happiness, and a continuation of his extraordinarily deep and original contributions to mathematics. I. M. Singer Contents Real and Complex Geometry in Four Dimensions M. F. ATIYAH. . . . . . . . . . . . . Equivariant Morse Theory and the Yang-Mills Equation on Riemann Surfaces RAOUL BaTT .. 11 Isometric Families of Kahler Structures EUGENIO CALABI. . 23 Two Applications of Algebraic Geometry to Entire Holomorphic Mappings MARK GREEN AND PHILLIP GRIFFITHS. • . . . • . . 41 The Canonical Map for Certain Hilbert Modular Surfaces F. HIRZEBRUCH . . . . . • . . . . . . . . . 75 Tight Embeddings and Maps. Submanifolds of Geometrical Class Three in EN NICOLAAS H. KUIPER .
Author |
: Manfredo P. do Carmo |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 492 |
Release |
: 2012-04-02 |
ISBN-10 |
: 9783642255885 |
ISBN-13 |
: 3642255884 |
Rating |
: 4/5 (85 Downloads) |
Synopsis Manfredo P. do Carmo – Selected Papers by : Manfredo P. do Carmo
This volume of selected academic papers demonstrates the significance of the contribution to mathematics made by Manfredo P. do Carmo. Twice a Guggenheim Fellow and the winner of many prestigious national and international awards, the professor at the institute of Pure and Applied Mathematics in Rio de Janeiro is well known as the author of influential textbooks such as Differential Geometry of Curves and Surfaces. The area of differential geometry is the main focus of this selection, though it also contains do Carmo's own commentaries on his life as a scientist as well as assessment of the impact of his researches and a complete list of his publications. Aspects covered in the featured papers include relations between curvature and topology, convexity and rigidity, minimal surfaces, and conformal immersions, among others. Offering more than just a retrospective focus, the volume deals with subjects of current interest to researchers, including a paper co-authored with Frank Warner on the convexity of hypersurfaces in space forms. It also presents the basic stability results for minimal surfaces in the Euclidean space obtained by the author and his collaborators. Edited by do Carmo's first student, now a celebrated academic in her own right, this collection pays tribute to one of the most distinguished mathematicians.
Author |
: Serguei Germanovich Bobkov |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 127 |
Release |
: 1997 |
ISBN-10 |
: 9780821806425 |
ISBN-13 |
: 0821806424 |
Rating |
: 4/5 (25 Downloads) |
Synopsis Some Connections between Isoperimetric and Sobolev-type Inequalities by : Serguei Germanovich Bobkov
For Borel probability measures on metric spaces, this text studies the interplay between isoperimetric and Sobolev-type inequalities. In particular the question of finding optimal constants via isoperimetric quantities is explored. Also given are necessary and sufficient conditions for the equivalence between the extremality of some sets in the isoperimetric problem and the validity of some analytic inequalities. The book devotes much attention to: the probability distributions on the real line; the normalized Lebesgue measure on the Euclidean sheres; and the canonical Gaussian measure on the Euclidean space.
Author |
: William K. Allard |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 482 |
Release |
: 1986 |
ISBN-10 |
: 9780821814703 |
ISBN-13 |
: 0821814702 |
Rating |
: 4/5 (03 Downloads) |
Synopsis Geometric Measure Theory and the Calculus of Variations by : William K. Allard
Includes twenty-six papers that survey a cross section of work in modern geometric measure theory and its applications in the calculus of variations. This title provides an access to the material, including introductions and summaries of many of the authors' much longer works and a section containing 80 open problems in the field.
Author |
: Gilles Royer |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 132 |
Release |
: 2007 |
ISBN-10 |
: 0821844016 |
ISBN-13 |
: 9780821844014 |
Rating |
: 4/5 (16 Downloads) |
Synopsis An Initiation to Logarithmic Sobolev Inequalities by : Gilles Royer
This is an introduction to logarithmic Sobolev inequalities with some important applications to mathematical statistical physics. Royer begins by gathering and reviewing the necessary background material on selfadjoint operators, semigroups, Kolmogorov diffusion processes, and solutions of stochastic differential equations.
Author |
: Catherine Bandle |
Publisher |
: Pitman Publishing |
Total Pages |
: 248 |
Release |
: 1980 |
ISBN-10 |
: UOM:39015015622353 |
ISBN-13 |
: |
Rating |
: 4/5 (53 Downloads) |
Synopsis Isoperimetric Inequalities and Applications by : Catherine Bandle
Author |
: José M. Mazón |
Publisher |
: Springer |
Total Pages |
: 138 |
Release |
: 2019-04-10 |
ISBN-10 |
: 9783030062439 |
ISBN-13 |
: 3030062430 |
Rating |
: 4/5 (39 Downloads) |
Synopsis Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets by : José M. Mazón
This book highlights the latest developments in the geometry of measurable sets, presenting them in simple, straightforward terms. It addresses nonlocal notions of perimeter and curvature and studies in detail the minimal surfaces associated with them. These notions of nonlocal perimeter and curvature are defined on the basis of a non-singular kernel. Further, when the kernel is appropriately rescaled, they converge toward the classical perimeter and curvature as the rescaling parameter tends to zero. In this way, the usual notions can be recovered by using the nonlocal ones. In addition, nonlocal heat content is studied and an asymptotic expansion is obtained. Given its scope, the book is intended for undergraduate and graduate students, as well as senior researchers interested in analysis and/or geometry.
Author |
: Yurii D. Burago |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 346 |
Release |
: 2013-03-14 |
ISBN-10 |
: 9783662074411 |
ISBN-13 |
: 3662074419 |
Rating |
: 4/5 (11 Downloads) |
Synopsis Geometric Inequalities by : Yurii D. Burago
A 1988 classic, covering Two-dimensional Surfaces; Domains on the Plane and on Surfaces; Brunn-Minkowski Inequality and Classical Isoperimetric Inequality; Isoperimetric Inequalities for Various Definitions of Area; and Inequalities Involving Mean Curvature.