Cube normalized symplectic capacities

TL;DR

This paper introduces cube normalization for symplectic capacities, establishes an analogue of the Viterbo conjecture for toric domains, and provides explicit formulas for the Lagrangian capacity in certain cases.

Contribution

It proposes a new cube normalization condition for symplectic capacities and proves an analogue of the Viterbo conjecture for monotone toric domains.

Findings

Cube normalization is satisfied by the Lagrangian and cube capacities.

An analogue of the strong Viterbo conjecture is established for monotone toric domains.

Explicit formulas for the Lagrangian capacity are derived for a broad class of toric domains.

Abstract

We introduce a new normalization condition for symplectic capacities, which we call cube normalization. This condition is satisfied by the Lagrangian capacity and the cube capacity. Our main result is an analogue of the strong Viterbo conjecture for monotone toric domains in all dimensions. Moreover, we give a family of examples where standard normalized capacities coincide but not cube normalized ones. Along the way, we give an explicit formula for the Lagrangian capacity on a large class of toric domains.