Isoperimetric Inequalities Involving Generalized Mean Curvature
Title | Isoperimetric Inequalities Involving Generalized Mean Curvature PDF eBook |
Author | Sven Winklmann |
Publisher | |
Pages | 11 |
Release | 2002 |
Genre | |
ISBN |
Mean Curvature Flow and Isoperimetric Inequalities
Title | Mean Curvature Flow and Isoperimetric Inequalities PDF eBook |
Author | Manuel Ritoré |
Publisher | Springer Science & Business Media |
Pages | 113 |
Release | 2010-01-01 |
Genre | Mathematics |
ISBN | 3034602138 |
Geometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface evolution in certain physical models. This is related to the property that such a flow is the gradient flow of the area functional and therefore appears naturally in problems where a surface energy is minimized. The mean curvature flow also has many geometric applications, in analogy with the Ricci flow of metrics on abstract riemannian manifolds. One can use this flow as a tool to obtain classification results for surfaces satisfying certain curvature conditions, as well as to construct minimal surfaces. Geometric flows, obtained from solutions of geometric parabolic equations, can be considered as an alternative tool to prove isoperimetric inequalities. On the other hand, isoperimetric inequalities can help in treating several aspects of convergence of these flows. Isoperimetric inequalities have many applications in other fields of geometry, like hyperbolic manifolds.
Isoperimetric Inequalities in Riemannian Manifolds
Title | Isoperimetric Inequalities in Riemannian Manifolds PDF eBook |
Author | Manuel Ritoré |
Publisher | Springer Nature |
Pages | 470 |
Release | 2023-10-06 |
Genre | Mathematics |
ISBN | 3031379012 |
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.
Isoperimetric Inequalities in the Theory of Surfaces of Bounded External Curvature
Title | Isoperimetric Inequalities in the Theory of Surfaces of Bounded External Curvature PDF eBook |
Author | Iurii D. Burago |
Publisher | Springer |
Pages | 118 |
Release | 1970 |
Genre | Juvenile Nonfiction |
ISBN |
Geometric Inequalities
Title | Geometric Inequalities PDF eBook |
Author | Yurii D. Burago |
Publisher | Springer |
Pages | 334 |
Release | 2010-12-01 |
Genre | Mathematics |
ISBN | 9783642057243 |
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.
Isoperimetric Inequalities and Applications
Title | Isoperimetric Inequalities and Applications PDF eBook |
Author | Catherine Bandle |
Publisher | Pitman Publishing |
Pages | 248 |
Release | 1980 |
Genre | Mathematics |
ISBN |
Topics in the Calculus of Variations
Title | Topics in the Calculus of Variations PDF eBook |
Author | Martin Fuchs |
Publisher | Springer Science & Business Media |
Pages | 155 |
Release | 2012-12-06 |
Genre | Technology & Engineering |
ISBN | 3322865282 |
This book illustrates two basic principles in the calculus of variations which are the question of existence of solutions and closely related the problem of regularity of minimizers. Chapter one studies variational problems for nonquadratic energy functionals defined on suitable classes of vectorvalued functions where also nonlinear constraints are incorporated. Problems of this type arise for mappings between Riemannian manifolds or in nonlinear elasticity. Using direct methods the existence of generalized minimizers is rather easy to establish and it is then shown that regularity holds up to a set of small measure. Chapter two contains a short introduction into Geometric Measure Theory which serves as a basis for developing an existence theory for (generalized) manifolds with prescribed mean curvature form and boundary in arbitrary dimensions and codimensions. One major aspect of the book is to concentrate on techniques and to present methods which turn out to be useful for applications in regularity theorems as well as for existence problems.