A regularity theory for multiple-valued Dirichlet minimizing maps

Details A regularity theory for multiple-valued Dirichlet minimizing maps A regularity theory for multiple-valued Dirichlet minimizing maps

2006-08-07

arxiv.org/abs/math/0608178v1

Mathematics

Optimization and Control

27 pages

Scientific paper

This paper discusses the regularity of multiple-valued Dirichlet minimizing maps into the sphere. It shows that even at branched point, as long as the normalized energy is small enough, we have the energy decay estimate. Combined with the previous work by Chun-Chi Lin, we get our first estimate that m-2 dimensional Hausdorff measure of singular set is zero. Furthermore, by looking at the tangent map and using dimension reduction argument, we show that the singular set is at least of codimension 3.

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