TY - JOUR
T1 - Remarks on symplectic capacities of p-products
AU - Haim-Kislev, Pazit
AU - Ostrover, Yaron
N1 - Publisher Copyright:
© 2023 World Scientific Publishing Company.
PY - 2023/3/1
Y1 - 2023/3/1
N2 - In this paper, we study the behavior of symplectic capacities of convex domains in the classical phase space with respect to symplectic p-products. As an application, by using a "tensor power trick", we show that it is enough to prove the weak version of Viterbo's volume-capacity conjecture in the asymptotic regime, i.e. when the dimension is sent to infinity. In addition, we introduce a conjecture about higher-order capacities of p-products, and show that if it holds, then there are no nontrivial p-decompositions of the symplectic ball.
AB - In this paper, we study the behavior of symplectic capacities of convex domains in the classical phase space with respect to symplectic p-products. As an application, by using a "tensor power trick", we show that it is enough to prove the weak version of Viterbo's volume-capacity conjecture in the asymptotic regime, i.e. when the dimension is sent to infinity. In addition, we introduce a conjecture about higher-order capacities of p-products, and show that if it holds, then there are no nontrivial p-decompositions of the symplectic ball.
KW - Symplectic capacities
KW - Viterbo's volume-capacity conjecture
KW - p-products
UR - http://www.scopus.com/inward/record.url?scp=85151835314&partnerID=8YFLogxK
U2 - 10.1142/S0129167X23500210
DO - 10.1142/S0129167X23500210
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AN - SCOPUS:85151835314
SN - 0129-167X
VL - 34
JO - International Journal of Mathematics
JF - International Journal of Mathematics
IS - 4
M1 - 2350021
ER -