Remarks on a Class of Solutions to the Minimal Surface System

Details Remarks on a Class of Solutions to the Minimal Surface System Remarks on a Class of Solutions to the Minimal Surface System

2003-03-04

arxiv.org/abs/math/0303041v1

Mathematics

Differential Geometry

contribution to the Conference Proceedings of the 2002 Workshop on Geometric Evolution Equations held at the National Center f

Scientific paper

We discuss a special class of solutions to the minimal surface system. These are vector-valued functions that "decrease area" and are natural generalization of scalar functions. After defining area-decreasing maps, we show several classical results for the minimal surface equation can be generalized. We also conjecture the solvability of Dirichlet problems within the category of area-decreasing maps.

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