Allard type Boundary Regularity Theorem for Varifolds with $C^{1,α}$ Boundary

Details Allard type Boundary Regularity Theorem for Varifolds with $C^{1,α}$ Boundary Allard type Boundary Regularity Theorem for Varifolds with $C^{1,α}$ Boundary

2010-08-27

arxiv.org/abs/1008.4728v1

Mathematics

Analysis of PDEs

32 pages, no figures

Scientific paper

In this paper we show that Allard's boundary regularity theorem for general varifolds can be generalized in the case of $C^{1,\alpha}$ boundaries; in Allard's paper it is required that the boundary is $C^{1,1}$. The proof presented here is along the lines of the proof of Allard's interior regularity theorem found in Simon's book "Lectures on Geometric Measure Theory". In particular we give the proof in the case of a rectifiable varifold. In this way, we simplify the notation and the computations needed for the proof, without however weakening the original hypotheses in Allard's paper, because of the rectifiability theorem for varifolds.

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