# Radius estimates for Alexandrov space with boundary

## TL;DR

This paper investigates the radius and boundary volume estimates of Alexandrov spaces with positive or non-negative curvature and convex boundaries, extending known results and exploring rigidity conditions in this geometric setting.

## Contribution

It provides new radius estimates and boundary volume bounds for Alexandrov spaces with convex boundaries, including a non-negatively curved rigidity result.

## Key findings

- Radius bounds for positively curved Alexandrov spaces
- Boundary volume estimates for non-negatively curved spaces
- Rigidity conditions characterizing equality cases

## Abstract

In this note, we study the radius of positively curved or non-negatively curved Alexandrov space with strictly convex boundary, with convexity measured by the Base-Angle defined by Alexander and Bishop. We also estimate the volume of the boundary of non-negatively curved spaces as well as the rigidity case, which can be thought as a non-negatively curved version of a recent result of Grove-Petersen.