The sharp energy-capacity inequality on convex symplectic manifolds

TL;DR

This paper extends a fundamental inequality relating symplectic invariants, specifically the Hofer-Zehnder capacity and displacement energy, from closed to convex symplectic manifolds, advancing understanding in symplectic geometry.

Contribution

It generalizes the sharp energy-capacity inequality to convex symplectic manifolds, broadening its applicability in symplectic geometry.

Findings

Established the inequality for convex symplectic manifolds

Extended previous results from closed to convex cases

Provides new tools for symplectic invariants analysis

Abstract

In symplectic geometry, symplectic invariants are useful tools in studying symplectic phenomena. Hofer-Zehnder capacity and displacement energy are important symplectic invariants. Usher proved the so-called sharp energy-capacity inequality between Hofer-Zehnder capacity and the displacement energy for closed symplectic manifolds. In this paper, we extend the sharp energy-capacity inequality to convex symplectic manifolds.