Reverse isoperimetric inequalities for Lagrangian intersection Floer theory

2023/06/07 by Chassé, Jean-Philippe, Hicks, Jeff, Nho, Yoon Jae Nick
#32Q65 #32U05 #Complex Variables (math.CV) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2306.04761

Abstract

We extend Groman and Solomon's reverse isoperimetric inequality to pseudoholomorphic curves with punctures at the boundary and whose boundary components lie in a collection of Lagrangian submanifolds with intersections locally modelled on ℝⁿ∩ (ℝ^k× √(-1)ℝ^n-k) inside ℂⁿ. Our construction closely follows the methods used by Duval (2016) and Abouzaid (2021) and corrects an error appearing in the latter approach.

Related

• Relative isoperimetric inequalities for Lagrangian disks
• A reverse isoperimetric inequality for J-holomorphic curves
• Isoperimetric problems and lower bounds on curvature
• Isoperimetric inequalities in Riemann surfaces and graphs
• On a result by Y. Groman and J. P. Solomon