Approaching the isoperimetric problem in H^m_ℂ via the hyperbolic log-convex density conjecture

2022/07/30 by Silini, Lauro
#Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.00195

Abstract

We prove that geodesic balls centered at some base point are isoperimetric in the real hyperbolic space H_{\mathbb R}ⁿ endowed with a smooth, radial, strictly log-convex density on the volume and perimeter. This is an analogue of the result by G. R. Chambers for log-convex densities on \mathbb Rⁿ. As an application we prove that in any rank one symmetric space of non-compact type, geodesic balls are isoperimetric in a class of sets enjoying a suitable notion of radial symmetry.

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• Proof of the Log-Convex Density Conjecture
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