Minimal surfaces and Colding-Minicozzi entropy in complex hyperbolic space

TL;DR

This paper explores the asymptotic geometry of minimal submanifolds in complex hyperbolic space, linking Colding-Minicozzi entropy to CR-volume, and introduces new regularity notions for these submanifolds.

Contribution

It introduces new notions of asymptotic regularity for minimal submanifolds in complex hyperbolic space and relates entropy to geometric quantities derived from asymptotic behavior.

Findings

Established a relationship between Colding-Minicozzi entropy and CR-volume.

Defined asymptotic regularity notions for minimal Lagrangian submanifolds.

Analyzed the asymptotic geometry of minimal submanifolds in complex hyperbolic space.

Abstract

We study notions of asymptotic regularity for a class of minimal submanifolds of complex hyperbolic space that includes minimal Lagrangian submanifolds. As an application, we show a relationship between an appropriate formulation of Colding-Minicozzi entropy and a quantity we call the CR-volume that is computed from the asymptotic geometry of such submanifolds.