Stationary measures and rectifiability
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Submission date: 21. Mar. 2002 (revised version: May 2002)
published in: Calculus of variations and partial differential equations, 17 (2003) 4, p. 357-368
DOI number (of the published article): 10.1007/s00526-002-0173-x
MSC-Numbers: 49Q15, 49Q05, 58E20, 58E15
Keywords and phrases: rectifiability, minimal varifolds, p-harmonic maps, yang-mills connections
For integers , we consider -valued Radon measures on an open set which satisfy
for all . We show that under certain conditions, has an (n - p)-dimensional density everywhere, and the set of points of positive density is countably (n - p)-rectifiable. This simplifies the proofs of several rectifiability theorems involving varifolds with vanishing first variations, p-harmonic maps, or Yang-Mills connections.