TY - JOUR
T1 - Higher index symplectic capacities do not satisfy the symplectic Brunn-Minkowski inequality
AU - Kerman, Ely
AU - Liang, Yuanpu
N1 - Funding Information:
The first-named author is supported by a grant from the Simons Foundation.
Publisher Copyright:
© 2021, The Hebrew University of Jerusalem.
PY - 2021/10
Y1 - 2021/10
N2 - 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].
AB - 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].
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U2 - 10.1007/s11856-021-2172-7
DO - 10.1007/s11856-021-2172-7
M3 - Article
AN - SCOPUS:85109296785
SN - 0021-2172
VL - 245
SP - 27
EP - 38
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -