A Note on the Stability and Uniqueness for Solutions to the Minimal Surface System
Date Issued
2004-12-31
Date
2004-12-31
Author(s)
DOI
922115M002011
Abstract
In this note, we show that the solution to the Dirichlet problem for the
minimal surface system is unique in the space of distance-decreasing maps. This follows
as a corollary of the following stability theorem: if a minimal submanifold is the graph
of a (strictly) distance-decreasing map, then is (strictly) stable. We also give another
criterion for the stability which covers the codimension one case. All theorems are
proved in a more general setting, which concerns minimal maps between Riemannian
manifolds. The complete statements of the results appear in Theorem 3.1, Theorem 3.2,
and Theorem 4.1.
Publisher
臺北市：國立臺灣大學數學系暨研究所
Type
report
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