Isoperimetric inequalities in unbounded convex bodies

We consider the problem of minimizing the relative perimeter under a volume constraint in an unbounded convex body

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Hlavní autoři: Leonardi, Gian Paolo, Ritoré, Manuel, Vernadakis, Efstratios
Médium: E-kniha Kniha
Jazyk:angličtina
Vydáno: Providence, Rhode Island American Mathematical Society 2022
Vydání:1
Edice:Memoirs of the American Mathematical Society
Témata:
Boundary value problems
Calculus of variations and optimal control; optimization > Manifolds > Optimization of shapes other than minimal surfaces. msc
Convex and discrete geometry > General convexity > Inequalities and extremum problems. msc
Convex bodies
Isoperimetric inequalities
asymptotic cylinders
convex bodies
isoperimetric dimension
isoperimetric profile
isoperimetric regions
Isoperimetric inequalities
rigidity
ISBN:9781470451189, 1470451182
ISSN:0065-9266, 1947-6221
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  • List of symbols -- Introduction -- Convex bodies and finite perimeter sets -- Unbounded convex bodies of uniform geometry -- A generalized existence result -- Concavity of the isoperimetric profile -- Sharp isoperimetric inequalities and isoperimetric rigidity -- Asymptotic behavior of the isoperimetric profile of an unbounded convex body
  • 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 -- Back Cover