Q-valued functions revisited
Analysis of PDEs
2011-03-18 v4
Abstract
In this note we revisit Almgren's theory of Q-valued functions, that are functions taking values in the space of unordered Q-tuples of points in R^n. In particular: 1) we give shorter versions of Almgren's proofs of the existence of Dir-minimizing Q-valued functions, of their Hoelder regularity and of the dimension estimate of their singular set; 2) we propose an alternative intrinsic approach to these results, not relying on Almgren's biLipschitz embedding; 3) we improve upon the estimate of the singular set of planar Dir-minimizing functions by showing that it consists of isolated points.
Cite
@article{arxiv.0803.0060,
title = {Q-valued functions revisited},
author = {Camillo De Lellis and Emanuele Nunzio Spadaro},
journal= {arXiv preprint arXiv:0803.0060},
year = {2011}
}
Comments
84 pages, 3 figures; changes: few typos corrected, reformatted for submission