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Higher index symplectic capacities do not satisfy the symplectic Brunn-Minkowski inequality
Israel Journal of Mathematics ( IF 0.8 ) Pub Date : 2021-07-02 , DOI: 10.1007/s11856-021-2172-7 Ely Kerman 1 , Yuanpu Liang 1
中文翻译:
更高指数的辛容量不满足辛 Brunn-Minkowski 不等式
更新日期:2021-07-04
Israel Journal of Mathematics ( IF 0.8 ) Pub Date : 2021-07-02 , DOI: 10.1007/s11856-021-2172-7 Ely Kerman 1 , Yuanpu Liang 1
Affiliation
In [1], Artstein-Avidan and Ostrover establish a symplectic version of the classical Brunn-Minkowski inequality where the role of the volume is played by the Ekeland-Hofer-Zehnder capacity. Here we prove that this symplectic Brunn-Minkowski inequality fails to hold for all of the higher index symplectic capacities defined by Gutt and Hutchings in [5].
中文翻译:
更高指数的辛容量不满足辛 Brunn-Minkowski 不等式
在 [1] 中,Artstein-Avidan 和 Ostrover 建立了经典 Brunn-Minkowski 不等式的辛版本,其中体积的作用由 Ekeland-Hofer-Zehnder 容量扮演。在这里,我们证明这种辛 Brunn-Minkowski 不等式不适用于 Gutt 和 Hutchings 在 [5] 中定义的所有更高指数辛容量。