Diameters of Ball Intersections

TL;DR

This paper proves that in a Riemannian manifold, the diameter of the intersection of two convex balls decreases continuously as their centers move farther apart.

Contribution

It establishes a new property of convex ball intersections in Riemannian geometry, showing the diameter behavior under center displacement.

Findings

Diameter decreases continuously with increasing center distance

Intersection becomes smaller as centers move apart

Provides insights into convex geometry in Riemannian manifolds

Abstract

We prove the diameter of the intersection of two closed convex balls in a Riemannian manifold eventually decreases continuously as the centers of the balls move apart.