Author: Gian Paolo Leonardi
Publisher:
ISBN: 9781470470203
Category : Convex bodies
Languages : en
Pages : 0
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
Author: Gian Paolo Leonardi
Publisher:
ISBN: 9781470470203
Category : Convex bodies
Languages : en
Pages : 0
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.
Publisher:
ISBN: 9781470470203
Category : Convex bodies
Languages : en
Pages : 0
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
Author: Gian Paolo Leonardi
Publisher: American Mathematical Society
ISBN: 1470451182
Category : Mathematics
Languages : en
Pages : 86
Book Description
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Publisher: American Mathematical Society
ISBN: 1470451182
Category : Mathematics
Languages : en
Pages : 86
Book Description
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Isoperimetric Inequalities in Riemannian Manifolds
Author: Manuel Ritoré
Publisher: Springer Nature
ISBN: 3031379012
Category : Mathematics
Languages : en
Pages : 470
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.
Publisher: Springer Nature
ISBN: 3031379012
Category : Mathematics
Languages : en
Pages : 470
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
Author: Jacob Bedrossian
Publisher: American Mathematical Society
ISBN: 1470472252
Category : Mathematics
Languages : en
Pages : 148
Book Description
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Publisher: American Mathematical Society
ISBN: 1470472252
Category : Mathematics
Languages : en
Pages : 148
Book Description
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Cancellation for surfaces revisited
Author: H. Flenner
Publisher: American Mathematical Society
ISBN: 1470453738
Category : Mathematics
Languages : en
Pages : 124
Book Description
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Publisher: American Mathematical Society
ISBN: 1470453738
Category : Mathematics
Languages : en
Pages : 124
Book Description
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Partial Compactification of Monopoles and Metric Asymptotics
Author: Chris Kottke
Publisher: American Mathematical Society
ISBN: 1470455412
Category : Mathematics
Languages : en
Pages : 124
Book Description
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Publisher: American Mathematical Society
ISBN: 1470455412
Category : Mathematics
Languages : en
Pages : 124
Book Description
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Decorated Dyck Paths, Polyominoes, and the Delta Conjecture
Author: Michele D’Adderio
Publisher: American Mathematical Society
ISBN: 1470471574
Category : Mathematics
Languages : en
Pages : 138
Book Description
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Publisher: American Mathematical Society
ISBN: 1470471574
Category : Mathematics
Languages : en
Pages : 138
Book Description
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Intrinsic Approach to Galois Theory of $q$-Difference Equations
Author: Lucia Di Vizio
Publisher: American Mathematical Society
ISBN: 1470453843
Category : Mathematics
Languages : en
Pages : 88
Book Description
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Publisher: American Mathematical Society
ISBN: 1470453843
Category : Mathematics
Languages : en
Pages : 88
Book Description
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Horocycle Dynamics: New Invariants and Eigenform Loci in the Stratum $mathcal {H}(1,1)$
Author: Matthew Bainbridge
Publisher: American Mathematical Society
ISBN: 1470455390
Category : Mathematics
Languages : en
Pages : 112
Book Description
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Publisher: American Mathematical Society
ISBN: 1470455390
Category : Mathematics
Languages : en
Pages : 112
Book Description
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One-Dimensional Dyadic Wavelets
Author: Peter M. Luthy
Publisher: American Mathematical Society
ISBN: 1470453746
Category : Mathematics
Languages : en
Pages : 168
Book Description
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Publisher: American Mathematical Society
ISBN: 1470453746
Category : Mathematics
Languages : en
Pages : 168
Book Description
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