Higher index symplectic capacities do not satisfy the symplectic Brunn-Minkowski inequality (Q2066127)
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scientific article; zbMATH DE number 7456838
| Language | Label | Description | Also known as |
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| English | Higher index symplectic capacities do not satisfy the symplectic Brunn-Minkowski inequality |
scientific article; zbMATH DE number 7456838 |
Statements
Higher index symplectic capacities do not satisfy the symplectic Brunn-Minkowski inequality (English)
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13 January 2022
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\textit{S. Artstein-Avidan} and \textit{Y. Ostrover} [Int. Math. Res. Not. 2008, Article ID rnn044, 31 p. (2008; Zbl 1149.52006)] proved a symplectic analogue of the Brunn-Minkowski inequality where the volume is replaced by the Ekeland-Hofer-Zehnder capacity. It is shown that such a symplectic Brunn-Minkowski inequality does not exist for all of the higher-index symplectic capacities recently introduced by \textit{J. Gutt} and \textit{M. Hutchings} [Algebr. Geom. Topol. 18, No. 6, 3537--3600 (2018; Zbl 1411.53062)].
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Ekeland-Hofer-Zehnder capacity
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Brunn-Minkowski inequality
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Gutt-Hutchings capacities
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