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Coisotropic Hofer–Zehnder capacities of convex domains and related results

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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.

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Acknowledgements

We are also deeply grateful to the anonymous referees for giving very helpful comments and suggestions to improve the exposition.

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Authors and Affiliations

  1. Department of Mathematics, Civil Aviation University of China, Tianjin, 300300, People’s Republic of China

    Rongrong Jin

  2. Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People’s Republic of China

    Guangcun Lu

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  1. Rongrong Jin
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Dedicated to Professor Leonid Polterovich on the occasion of his sixtieth birthday.

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Rongrong Jin was partially supported by Scientific Research Foundation of CAUC (No: 2020KYQD107).

Partially supported by the NNSF 11271044 of China.

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Jin, R., Lu, G. Coisotropic Hofer–Zehnder capacities of convex domains and related results. J. Fixed Point Theory Appl. 25, 54 (2023). https://doi.org/10.1007/s11784-023-01056-w

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