A note on the capacities of Lagrangian $p$-sum

Abstract

In this short note, we construct an explicit embedding of the rescaling of the $p$-sum $K{\oplus }_p{K}^{\circ }$ of the centrally symmetric convex domain $K$ and its polar $K^{\circ }$ to the product $K\times K^{\circ }$. The rescaling constant is sharp in some cases. Additionally, we comment on the strong Viterbo conjecture for $K{\oplus }_p{K}^{\circ }$.

7 pages, 1 figure

References in corpus (5)

• From Symplectic Measurements to the Mahler Conjecture
• Estimating symplectic capacities from lengths of closed curves on the unit spheres
• Remarks on symplectic capacities of $p$-products
• Riemannian distance and symplectic embeddings in cotangent bundle
• On the agreement of symplectic capacities in high dimension