Deformations of Asymptotically Conical Special Lagrangian Submanifolds

TL;DR

This paper investigates the deformation theory of non-compact, asymptotically conical special Lagrangian submanifolds, extending McLean's results from the compact case to non-compact settings with boundary conditions at infinity.

Contribution

It develops a framework for understanding deformations of asymptotically conical special Lagrangian submanifolds considering various boundary conditions at infinity.

Findings

Deformation spaces depend on asymptotic boundary conditions.

Extension of McLean's theory to non-compact submanifolds.

Identification of moduli space dimensions based on topology and asymptotics.

Abstract

McLean studied the deformations of compact special Lagrangian submanifolds, showing in particular that they come in moduli spaces whose dimension depends only on the topology of the submanifold. In this article we study the analogous problem for non-compact, "asymptotically conical" SL submanifolds, with respect to various "boundary conditions at infinity".