Uniqueness of Minimal Graph in General Codimension
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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.
The first two authors are supported by 102-2115-M-002-013-MY3, and the last author is supported by 105-2115-M-002-006-MY2. The second author would like to thank Kai-Wei Zhao and Wei-Bo Su for their interests and discussions.