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Isoperimetric and Stable Sets for Log-Concave Perturbations of Gaussian Measures

César Rosales (2014)

Analysis and Geometry in Metric Spaces

Let be an open half-space or slab in ℝn+1 endowed with a perturbation of the Gaussian measure of the form f (p) := exp(ω(p) − c|p|2), where c > 0 and ω is a smooth concave function depending only on the signed distance from the linear hyperplane parallel to ∂ Ω. In this work we follow a variational approach to show that half-spaces perpendicular to ∂ Ω uniquely minimize the weighted perimeter in Ω among sets enclosing the same weighted volume. The main ingredient of the proof is the characterization...

Isoperimetric Regions in Rnwith Density rp

Wyatt Boyer, Bryan Brown, Gregory R. Chambers, Alyssa Loving, Sarah Tammen (2016)

Analysis and Geometry in Metric Spaces

We show that the unique isoperimetric regions in Rn with density rp for n ≥ 3 and p > 0 are balls with boundary through the origin.

Iterative algorithms for variational inclusions, mixed equilibrium and fixed point problems with application to optimization problems

Yonghong Yao, Yeol Cho, Yeong-Cheng Liou (2011)

Open Mathematics

In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of a nonexpansive mapping, and the the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets, which is a solution of a certain optimization problem related to a strongly positive bounded linear operator....

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