Widths of balls and free boundary minimal submanifolds

TL;DR

This paper establishes that the k-dimensional width of an n-ball in a space form equals the area of an equatorial k-ball and explores lower bounds for free boundary minimal submanifolds in such settings.

Contribution

It provides a precise characterization of widths of n-balls and introduces new lower bounds for areas of free boundary minimal submanifolds in space form balls.

Findings

k-dimensional width of n-ball equals equatorial k-ball area

Derived lower bounds for free boundary minimal submanifold areas

Enhanced understanding of geometric properties in space form balls

Abstract

We observe that the $k$-dimensional width of an $n$-ball in a space form is given by the area of an equatorial $k$-ball. We also investigate related lower bounds for the area of a free boundary minimal submanifold in a space form ball.