Remarks on the equality case of the Bonnesen inequality

TL;DR

This paper discusses the conditions under which equality holds in the high-dimensional Bonnesen inequality for sections, and relates it to the known equality case for projections, providing new insights into geometric inequalities.

Contribution

It offers a new argument for the equality case of the high-dimensional Bonnesen inequality for sections and connects it to the projection case.

Findings

Provides a proof for the equality case of the Bonnesen inequality for sections.

Shows the known equality case for projections as a consequence.

Enhances understanding of geometric inequalities in high dimensions.

Abstract

An argument is provided for the equality case of the high dimensional Bonnesen inequality for sections. The known equality case of the Bonnesen inequality for projections is presented as a consequence.