Stability of the isodiametric problem on the sphere and in the hyperbolic space

TL;DR

This paper establishes a stability version of the isodiametric inequality in spherical and hyperbolic geometries, providing insights into how near-optimal shapes behave in these curved spaces.

Contribution

It introduces a stability result for the isodiametric inequality specifically on the sphere and in hyperbolic space, extending classical Euclidean results.

Findings

Proved a stability version of the isodiametric inequality on the sphere.

Extended stability results to hyperbolic space.

Provided quantitative bounds on deviations from optimal shapes.

Abstract

We prove a stability version of the isodiametric inequality on the sphere and in the hyperbolic space.