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Isoperimetric Inequalities in Riemannian Manifolds de Manuel Ritoré

Isoperimetric Inequalities in Riemannian Manifolds: Progress in Mathematics, cartea 348

Autor Manuel Ritoré
en Limba Engleză Hardback – 7 oct 2023
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.
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Specificații

ISBN-13: 9783031379000
ISBN-10: 3031379004
Pagini: 460
Ilustrații: XVIII, 460 p. 28 illus., 1 illus. in color.
Dimensiuni: 155 x 235 mm
Greutate: 0.84 kg
Ediția:1st ed. 2023
Editura: Springer International Publishing
Colecția Birkhäuser
Seria Progress in Mathematics

Locul publicării:Cham, Switzerland

Cuprins

- 1. Introduction. - 2. Isoperimetric Inequalities in Surfaces. - 3. The Isoperimetric Profile of Compact Manifolds. - 4. The Isoperimetric Profile of Non-compact Manifolds. - 5. Symmetrization and Classical Results. - 6. Space Forms. - 7. The Isoperimetric Profile for Small and Large Volumes. - 8. Isoperimetric Comparison for Sectional Curvature. - 9. Relative Isoperimetric Inequalities.

Notă biografică

Manuel Ritoré is professor of Mathematics at the University of Granada since 2007. His earlier research focused on geometric inequalities in Riemannian manifolds, specially on those of isoperimetric type. In this field he has obtained some results such as a classification of isoperimetric sets in the 3-dimensional real projective space; a classification of 3-dimensional double bubbles; existence of solutions of the Allen-Cahn equation near non-degenerate minimal surfaces; an alternative proof of the isoperimetric conjecture for 3-dimensional Cartan-Hadamard manifolds; optimal isoperimetric inequalities outside convex sets in the Euclidean space; and a characterization of isoperimetric regions of large volume in Riemannian cylinders, among others. Recently, he has become interested on geometric variational problems in spaces with less regularity, such as sub-Riemannian manifolds or more general metric measure spaces, where he has obtained a classification of isoperimetric sets inthe first Heisenberg group under regularity assumptions, and Brunn-Minkowski inequalities for metric measure spaces, among others.

Textul de pe ultima copertă

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.

Caracteristici

Written in a clear and appealing style Collects results obtained over the last 25 years Includes a great deal of introductory material