Uniqueness of Minimal Graph in General Codimension
Journal
Journal of Geometric Analysis
Journal Volume
29
Journal Issue
1
Pages
121-133
Date Issued
2019
Author(s)
Abstract
In this paper, we obtain the uniqueness of general codimension Dirichlet problem for minimal surface system in restricted classes. The condition is in terms of singular values and in particular covers the classical hypersurface case and earlier results in higher codimension. To prove the uniqueness result, a natural way is to consider the geodesic homotopy of two solutions. However, the singular values for linear combination of maps are not clear. We apply majorization techniques from convex optimisation to overcome the difficulties.
Type
journal article