Remarks on the systoles of symmetric convex hypersurfaces and symplectic capacities

Joontae Kim; Seongchan Kim; Myeonggi Kwon

doi:10.1007/s11784-022-00953-w

Remarks on the systoles of symmetric convex hypersurfaces and symplectic capacities

Joontae Kim
, Seongchan Kim
, Myeonggi Kwon^*

^*Corresponding author for this work

Department of Mathematics Education

Sogang University
Kongju National University
Sunchon National University

Research output: Contribution to journal › Journal article › peer-review

4 Scopus citations

Abstract

In this note we study the systoles of convex hypersurfaces in R²ⁿ invariant under an anti-symplectic involution. We investigate a uniform upper bound of the ratio between the systole and the symmetric systole of the hypersurfaces using symplectic capacities from Floer theory. We discuss various concrete examples in which the ratio can be understood explicitly.

Original language	English
Article number	28
Journal	Journal of Fixed Point Theory and Applications
Volume	24
Issue number	2
DOIs	https://doi.org/10.1007/s11784-022-00953-w
State	Published - 2022.06

Keywords

real symplectic capacities
symmetric periodic orbits
Systoles

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10.1007/s11784-022-00953-w

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title = "Remarks on the systoles of symmetric convex hypersurfaces and symplectic capacities",

abstract = "In this note we study the systoles of convex hypersurfaces in R2n invariant under an anti-symplectic involution. We investigate a uniform upper bound of the ratio between the systole and the symmetric systole of the hypersurfaces using symplectic capacities from Floer theory. We discuss various concrete examples in which the ratio can be understood explicitly.",

keywords = "real symplectic capacities, symmetric periodic orbits, Systoles",

author = "Joontae Kim and Seongchan Kim and Myeonggi Kwon",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2022",

month = jun,

doi = "10.1007/s11784-022-00953-w",

language = "English",

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T1 - Remarks on the systoles of symmetric convex hypersurfaces and symplectic capacities

AU - Kim, Joontae

AU - Kim, Seongchan

AU - Kwon, Myeonggi

PY - 2022/6

Y1 - 2022/6

N2 - In this note we study the systoles of convex hypersurfaces in R2n invariant under an anti-symplectic involution. We investigate a uniform upper bound of the ratio between the systole and the symmetric systole of the hypersurfaces using symplectic capacities from Floer theory. We discuss various concrete examples in which the ratio can be understood explicitly.

AB - In this note we study the systoles of convex hypersurfaces in R2n invariant under an anti-symplectic involution. We investigate a uniform upper bound of the ratio between the systole and the symmetric systole of the hypersurfaces using symplectic capacities from Floer theory. We discuss various concrete examples in which the ratio can be understood explicitly.

KW - real symplectic capacities

KW - symmetric periodic orbits

KW - Systoles

UR - https://www.scopus.com/pages/publications/85128053789

U2 - 10.1007/s11784-022-00953-w

DO - 10.1007/s11784-022-00953-w

M3 - Journal article

AN - SCOPUS:85128053789

SN - 1661-7738

VL - 24

JO - Journal of Fixed Point Theory and Applications

JF - Journal of Fixed Point Theory and Applications

IS - 2

M1 - 28

ER -

Remarks on the systoles of symmetric convex hypersurfaces and symplectic capacities

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Keywords

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