Maximal Weinstein neighborhoods of symmetric R-spaces and their symplectic capacities

TL;DR

This paper investigates the symplectic geometry of symmetric R-spaces, demonstrating that their maximal Weinstein neighborhoods are dense and computing key symplectic capacities of associated cotangent bundles.

Contribution

It introduces the density of maximal Weinstein neighborhoods for symmetric R-spaces and calculates their Gromov width and Hofer--Zehnder capacity.

Findings

Maximal Weinstein neighborhoods of symmetric R-spaces are dense.

Explicit computations of Gromov width for cotangent bundles.

Explicit computations of Hofer--Zehnder capacity for cotangent bundles.

Abstract

Symmetric R-spaces can be characterized as real forms of Hermitian symmetric spaces, and as such, they are all embedded as Lagrangian submanifolds. We show that their maximal Weinstein tubular neighborhoods are dense and use this property to compute both the Gromov width and the Hofer--Zehnder capacity of the corresponding disc (co)tangent bundles of the symmetric R-spaces.