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The M-ellipsoid, symplectic capacities and volume. (English) Zbl 1138.53060

Summary: In this work we bring together tools and ideology from two different fields, symplectic geometry and asymptotic geometric analysis, to arrive at some new results. Our main result is a dimension-independent bound for the symplectic capacity of a convex body by its volume radius.

MSC:

53D05 Symplectic manifolds (general theory)
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
46B07 Local theory of Banach spaces
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
46B20 Geometry and structure of normed linear spaces
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