Isoperimetric Inequalities in Unbounded Convex Bodies

Isoperimetric Inequalities in Unbounded Convex Bodies PDF Author: Gian Paolo Leonardi
Publisher:
ISBN: 9781470470203
Category : Convex bodies
Languages : en
Pages : 0

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Book Description
We consider the problem of minimizing the relative perimeter under a volume constraint in an unbounded convex body C c R^n , without assuming any further regularity on the boundary of C. Motivated by an example of an unbounded convex body with null isoperimetric profile, we introduce the concept of unbounded convex body with uniform geometry. We then provide a handy characterization of the uniform geometry property and, by exploiting the notion of asymptotic cylinder of C, we prove existence of isoperimetric regions in a generalized sense. By an approximation argument we show the strict concavity of the isoperimetric profile and, consequently, the connectedness of generalized isoperimetric regions. We also focus on the cases of small as well as of large volumes; in particular we show existence of isoperimetric regions with sufficiently large volumes, for special classes of unbounded convex bodies. We finally address some questions about isoperimetric rigidity and analyze the asymptotic behavior of the isoperimetric profile in connection with the notion of isoperimetric dimension.

Isoperimetric Inequalities in Unbounded Convex Bodies

Isoperimetric Inequalities in Unbounded Convex Bodies PDF Author: Gian Paolo Leonardi
Publisher:
ISBN: 9781470470203
Category : Convex bodies
Languages : en
Pages : 0

Get Book Here

Book Description
We consider the problem of minimizing the relative perimeter under a volume constraint in an unbounded convex body C c R^n , without assuming any further regularity on the boundary of C. Motivated by an example of an unbounded convex body with null isoperimetric profile, we introduce the concept of unbounded convex body with uniform geometry. We then provide a handy characterization of the uniform geometry property and, by exploiting the notion of asymptotic cylinder of C, we prove existence of isoperimetric regions in a generalized sense. By an approximation argument we show the strict concavity of the isoperimetric profile and, consequently, the connectedness of generalized isoperimetric regions. We also focus on the cases of small as well as of large volumes; in particular we show existence of isoperimetric regions with sufficiently large volumes, for special classes of unbounded convex bodies. We finally address some questions about isoperimetric rigidity and analyze the asymptotic behavior of the isoperimetric profile in connection with the notion of isoperimetric dimension.

Isoperimetric Inequalities in Unbounded Convex Bodies

Isoperimetric Inequalities in Unbounded Convex Bodies PDF Author: Gian Paolo Leonardi
Publisher: American Mathematical Society
ISBN: 1470451182
Category : Mathematics
Languages : en
Pages : 86

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Book Description
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Isoperimetric Inequalities in Riemannian Manifolds

Isoperimetric Inequalities in Riemannian Manifolds PDF Author: Manuel Ritoré
Publisher: Springer Nature
ISBN: 3031379012
Category : Mathematics
Languages : en
Pages : 470

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Book Description
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.

Dynamics Near the Subcritical Transition of the 3D Couette Flow II: Above Threshold Case

Dynamics Near the Subcritical Transition of the 3D Couette Flow II: Above Threshold Case PDF Author: Jacob Bedrossian
Publisher: American Mathematical Society
ISBN: 1470472252
Category : Mathematics
Languages : en
Pages : 148

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Cancellation for surfaces revisited

Cancellation for surfaces revisited PDF Author: H. Flenner
Publisher: American Mathematical Society
ISBN: 1470453738
Category : Mathematics
Languages : en
Pages : 124

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Partial Compactification of Monopoles and Metric Asymptotics

Partial Compactification of Monopoles and Metric Asymptotics PDF Author: Chris Kottke
Publisher: American Mathematical Society
ISBN: 1470455412
Category : Mathematics
Languages : en
Pages : 124

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Decorated Dyck Paths, Polyominoes, and the Delta Conjecture

Decorated Dyck Paths, Polyominoes, and the Delta Conjecture PDF Author: Michele D’Adderio
Publisher: American Mathematical Society
ISBN: 1470471574
Category : Mathematics
Languages : en
Pages : 138

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Intrinsic Approach to Galois Theory of $q$-Difference Equations

Intrinsic Approach to Galois Theory of $q$-Difference Equations PDF Author: Lucia Di Vizio
Publisher: American Mathematical Society
ISBN: 1470453843
Category : Mathematics
Languages : en
Pages : 88

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Horocycle Dynamics: New Invariants and Eigenform Loci in the Stratum $mathcal {H}(1,1)$

Horocycle Dynamics: New Invariants and Eigenform Loci in the Stratum $mathcal {H}(1,1)$ PDF Author: Matthew Bainbridge
Publisher: American Mathematical Society
ISBN: 1470455390
Category : Mathematics
Languages : en
Pages : 112

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One-Dimensional Dyadic Wavelets

One-Dimensional Dyadic Wavelets PDF Author: Peter M. Luthy
Publisher: American Mathematical Society
ISBN: 1470453746
Category : Mathematics
Languages : en
Pages : 168

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