Finiteness of the Hofer-Zehnder capacity of neighborhoods of symplectic submanifolds

Abstract

We use the minimal coupling procedure of Sternberg and Weinstein and our pseudo-symplectic capacity theory to prove that every closed symplectic submanifold in any symplectic manifold has an open neighborhood with finite (${\pi }_1$-sensitive) Hofer-Zehnder symplectic capacity. Consequently, the Weinstein conjecture holds near closed symplectic submanifolds in any symplectic manifold.

arXiv comment33 pages

References in corpus (1)

• Hofer-Zehnder semicapacity of cotangent bundles and symplectic submanifolds