A weighted isoperimetric inequality on the hyperbolic plane

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arxiv 1712.07690 v1 pith:3TLUQB45 submitted 2017-12-19 math.AP

I. McGillivray This is my paper · ORCID

classification math.AP

keywords hyperbolicplaneconjecturecounterpartdensityinequalityisoperimetriclog-convex

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We prove a counterpart of the log-convex density conjecture in the hyperbolic plane.

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Free energy minimizers with radial densities: classification and quantitative stability
math.AP 2024-12 conditional novelty 7.0 of 10

Centered spheres minimize the weighted free energy for all volumes only under extra monotonicity of both weights; otherwise the second-variation condition psi''+g' >= 0 can fail to select global minimizers.