On Lagrangian barriers and applications of Non-Squeezing

2025/07/27 by Vicente, Alejandro
#53D05 #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2507.20222

Abstract

In this note we show the existence of Lagrangian barriers in a certain class of domains in ℝ²ⁿ, including dual Lagrangian products and some ``sufficiently" round domains. Many of these results come as applications of the Non-Squeezing Theorem. We also give a new interesting application of the Non-Squeezing Theorem and the Symplectic Camel Theorem.

Citations

• The strong Viterbo conjecture and various flavours of duality in Lagrangian products
• On the Existence of Symplectic Barriers
• On the rigidity of lagrangian products
• The embedding capacity of 4-dimensional symplectic ellipsoids

Related

• An extension of Biran's Lagrangian barrier theorem
• Non-squeezing and capacities for some calibrated geometries
• Obstructions to the Existence and Squeezing of Lagrangian Cobordisms
• On the rigidity of lagrangian products
• Properties of squeezing functions and geometry of bounded domains