Calculus of Variations and Geometric Measure Theory

C. De Lellis - Emanuele Nunzio Spadaro

Q-valued functions revisited

created by delellis on 29 Feb 2008
modified on 27 Jun 2019


Published Paper

Inserted: 29 feb 2008
Last Updated: 27 jun 2019

Journal: Memoirs of the American Mathematical Society
Volume: 991
Year: 2011

ArXiv: 0803.0060 PDF


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 Rn. 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.