A Sharp Isoperimetric Property of the Renormalized Area of a Minimal Surface in Hyperbolic Space

TL;DR

This paper establishes a new inequality relating the renormalized area of minimal surfaces in hyperbolic space to the conformal length of their boundary, advancing understanding of geometric properties in hyperbolic geometry.

Contribution

It introduces a sharp isoperimetric inequality linking minimal surface area and boundary conformal length in hyperbolic space, a novel geometric relation.

Findings

Proves a bound on the renormalized area in terms of boundary length.

Establishes a sharp inequality with potential applications in geometric analysis.

Provides new insights into minimal surface theory in hyperbolic geometry.

Abstract

We prove an inequality bounding the renormalized area of a complete minimal surface in hyperbolic space in terms of the conformal length of its ideal boundary.