Convexity of solutions and Brunn-Minkowski inequalities for Hessian equations in \R³

2011/01/03 by Salani, Paolo · 3 citations
#35J60 #39B62 #47J05 #52A40 #52C25 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1101.0496

Abstract

By using Minkowski addition of convex functions, we prove convexity and rearrangement properties of solutions to some Hessian equations in \R³ and Brunn-Minkowski and isoperimetric inequalities for related functionals.

Cited by

• The p-th dual Minkowski problem for the k-torsional rigidity corresponding to a k-Hessian equation
• Explicit solutions to Christoffel-Minkowski problems and Hessian equations under rotational symmetries
• The strong log-concavity for first eigenfunction of the Ornstein-Uhlenbeck operator in the class of convex bodies

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• Generalized Minkowski inequality via degenerate Hessian equations on exterior domains
• Classical Neumann Problems for Hessian equations and Alexandrov-Fenchel's inequalities
• C² estimates for k-Hessian equations and a rigidity theorem
• Convexity of Hessian Integrals and Poincare Type Inequalities