Deformations of calibrated submanifolds with boundary

TL;DR

This paper reviews deformation theory for calibrated minimal submanifolds with boundary in special holonomy manifolds, extending McLean's results from closed to boundary cases.

Contribution

It extends McLean's deformation theory to include compact calibrated submanifolds with boundary constrained to a fixed submanifold.

Findings

Deformation theory for submanifolds with boundary in special holonomy manifolds.

Conditions for deformations when boundary is constrained.

Extension of classical results to boundary cases.

Abstract

We review some results concerning the deformations of calibrated minimal submanifolds which occur in Riemannian manifolds with special holonomy. The calibrated submanifolds are assumed compact with a non-empty boundary which is constrained to move in a particular fixed submanifold. The results extend McLean's deformation theory previously developed for closed compact submanifolds.