A weighted isoperimetric inequality on the hyperbolic plane

TL;DR

This paper establishes a new isoperimetric inequality in the hyperbolic plane, extending classical results to a setting with hyperbolic geometry and weighted measures.

Contribution

It proves a hyperbolic analogue of the log-convex density conjecture, providing new insights into geometric inequalities in non-Euclidean spaces.

Findings

Established a weighted isoperimetric inequality in the hyperbolic plane

Extended the log-convex density conjecture to hyperbolic geometry

Provided new tools for geometric analysis in curved spaces

Abstract

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