An Allard type regularity theorem for varifolds with Hölder continuous generalized normal

2013/11/15 by Theodora Bourni, Bourni, Theodora, Alexander Volkmann +1
Computer Science · Mathematics · #28A75 #49Q15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Point processes and geometric inequalities #math.AP #msc:28A75 #msc:49Q15

paper · pdf · doi:10.48550/arxiv.1311.3963

20 pages

arxiv created 2013/11/15 · openalex publication_date 2013/11/15 · arxiv updated 2013/11/18 · openalex created_date 2022/09/09 · openalex updated_date 2026/07/28

Abstract

We prove that Allard's regularity theorem holds for rectifiable n-dimensional varifolds V assuming a weaker condition on the first variation. This, in the special case when V is a smooth manifold translates to the following: If ω_n^-1ρ^-n\rm area(V∩ B_ρ(x)) is sufficiently close to 1 and the unit normal of V satisfies a C^0,α estimate, then V∩ B_ρ/2(x) is the graph of a C^1,α function with estimates. Furthermore, a similar boundary regularity theorem is true.

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