Volume difference inequalities

TL;DR

This paper establishes inequalities that relate the difference in volumes of two bodies to the differences in their section or projection areas, with extensions to arbitrary measures.

Contribution

It introduces new inequalities connecting volume differences with section and projection area differences, extending to arbitrary measures.

Findings

Inequalities estimating volume differences from section and projection areas.

Extensions of inequalities to arbitrary measures.

Provides bounds for volume differences based on geometric measures.

Abstract

We prove several inequalities estimating the distance between volumes of two bodies in terms of the maximal or minimal difference between areas of sections or projections of these bodies. We also provide extensions in which volume is replaced by an arbitrary measure.