The Brunn-Minkowski Inequality and A Minkowski Problem for Nonlinear Capacity

In this article we study two classical potential-theoretic problems in convex geometry. The first problem is an inequality of Brunn-Minkowski type for a nonlinear capacity, In the first part of this article, we prove the Brunn-Minkowski inequality for this capacity: In the second part of this articl...

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Bibliographic Details
Main Authors: Akman, Murat, Gong, Jasun, Hineman, Jay, Lewis, John, Vogel, Andrew
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2022
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
Inequalities (Mathematics)
Minkowski geometry
Nonlinear theories
Minkowski problem
The Brunn-Minkowski inequality
<inline-formula content-type="math/mathml"> A \mathcal {A} </inline-formula>-harmonic PDEs
inequalities and extremum problems
variational formula
Hadamard variational formula
nonlinear capacities
potentials and capacities
ISBN:1470450526, 9781470450526
ISSN:0065-9266, 1947-6221
Online Access:Get full text
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Summary:In this article we study two classical potential-theoretic problems in convex geometry. The first problem is an inequality of Brunn-Minkowski type for a nonlinear capacity, In the first part of this article, we prove the Brunn-Minkowski inequality for this capacity: In the second part of this article we study a Minkowski problem for a certain measure associated with a compact convex set
Bibliography:January 2022, volume 275, number 1348 (second of 6 numbers)
Includes bibliographical references (p. 113-115)
Other authors: Jasun Gong, Jay Hineman, John Lewis, Andrew Vogel
ISBN:1470450526
9781470450526
ISSN:0065-9266
1947-6221
DOI:10.1090/memo/1348