A regularity theory for multiple-valued Dirichlet minimizing maps
Optimization and Control
2007-05-23 v1 Analysis of PDEs
Abstract
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.
Cite
@article{arxiv.math/0608178,
title = {A regularity theory for multiple-valued Dirichlet minimizing maps},
author = {Wei Zhu},
journal= {arXiv preprint arXiv:math/0608178},
year = {2007}
}
Comments
27 pages