A Brunn-Minkowski Inequality for Symplectic Capacities of Convex Domains

TL;DR

This paper establishes a Brunn-Minkowski inequality within symplectic geometry, providing new insights into the behavior of symplectic capacities of convex domains and exploring their applications.

Contribution

It introduces a novel Brunn-Minkowski inequality for symplectic capacities, extending classical convex geometry results to symplectic settings.

Findings

Proved a Brunn-Minkowski-type inequality for symplectic capacities.

Demonstrated applications in symplectic geometry.

Extended convex geometric inequalities to symplectic contexts.

Abstract

In this work we prove a Brunn-Minkowski-type inequality in the context of symplectic geometry and discuss some of its applications.