Coisotropic Hofer-Zehnder capacities of convex domains and related results

Abstract

We prove representation formulas for the coisotropic Hofer-Zehnder capacities of bounded convex domains with special coisotropic submanifolds and the leaf relation (introduced by Lisi and Rieser recently), study their estimates and relations with the Hofer-Zehnder capacity,give some interesting corollaries, and also obtain corresponding versions of a Brunn-Minkowski type inequality by Artstein-Avidan and Ostrover and a theorem by Evgeni Neduv.

Latex, 52 pages; final version, to appear in Journal of Fixed Point Theory and Applications

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• On the symplectic size of convex polytopes
• Coisotropic Ekeland-Hofer capacities
• Viterbo's conjecture for certain Hamiltonians in classical mechanics
• Generalizations of Ekeland-Hofer and Hofer-Zehnder symplectic capacities and applications
• On the Almost Everywhere Continuity
• The Viterbo's capacity conjectures for convex toric domains and the product of a $1$-unconditional convex body and its polar

Cited by in corpus (1)

• Coisotropic Ekeland-Hofer capacities