Isoperimetric Inequalities in Unbounded Convex Bodies.

Cover
Title page
List of symbols
Chapter 1. Introduction
1.1. Historical background
1.2. Outline of contents
Chapter 2. Convex bodies and finite perimeter sets
2.1. Convex bodies and local convergence in Hausdorff distance
2.2. Finite perimeter sets and isoperimetric profile
Chapter 3. Unbounded convex bodies of uniform geometry
3.1. Asymptotic cylinders
3.2. Convex bodies of uniform geometry
3.3. Density estimates and a concentration lemma
3.4. Examples
Chapter 4. A generalized existence result
4.1. Preliminary results
4.2. The main result
Chapter 5. Concavity of the isoperimetric profile
5.1. Continuity of the isoperimetric profile
5.2. Approximation by smooth sets
5.3. Concavity of the isoperimetric profile
Chapter 6. Sharp isoperimetric inequalities and isoperimetric rigidity
6.1. Convex bodies with non-degenerate asymptotic cone
6.2. The isoperimetric profile for small volumes
6.3. Isoperimetric rigidity
Chapter 7. Asymptotic behavior of the isoperimetric profile of an unbounded convex body
7.1. An asymptotic isoperimetric inequality
7.2. Estimates on the volume growth of balls
7.3. Examples
Bibliography
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