Deformations of Asymptotically Cylindrical Special Lagrangian Submanifolds with Fixed Boundary

TL;DR

This paper investigates the deformation theory of asymptotically cylindrical special Lagrangian submanifolds within Calabi-Yau 3-folds, establishing conditions for smooth moduli spaces and computing their dimensions based on cohomological data.

Contribution

It provides new conditions on decay rates ensuring smoothness of the moduli space and relates its dimension to specific cohomology groups, advancing understanding of special Lagrangian deformations.

Findings

Moduli space is smooth under certain decay rate conditions.

Dimension of moduli space equals the dimension of a specific cohomology image.

Identifies conditions linking geometric decay rates to topological invariants.

Abstract

Given an asymptotically cylindrical special Lagrangian submanifold L in an asymptotically cylindrical Calabi-Yau 3-fold X, we determine conditions on a decay rate gamma which make the moduli space of (local) special Lagrangian deformations of L in X a smooth manifold and show that it has dimension equal to the dimension of the image of H^1_{cs}(L,R) in H^1(L,R) under the natural inclusion map.