Inradius estimates for convex domains in 2-dimensional Alexandrov spaces

TL;DR

This paper establishes precise lower bounds on inscribed ball radii for convex domains in 2D Alexandrov spaces with curvature constraints, and characterizes when these bounds are achieved.

Contribution

It provides sharp inradius estimates for convex domains in 2D Alexandrov spaces and characterizes the equality cases.

Findings

Sharp lower bounds on inscribed ball radii.

Characterization of equality cases.

Insights into convex geometry in Alexandrov spaces.

Abstract

We obtain sharp lower bounds on the radii of inscribed balls for strictly convex isoperimetric domains lying in a 2-dimensional Alexandrov metric space of curvature bounded below. We also characterize the case when such bounds are attained.