Critical Allard regularity: pointwise tilt-excess estimates

2024/02/20 by Sean McCurdy, McCurdy, Sean
Computer Science · Economics, Econometrics and Finance · Mathematics · #49Q15 (Primary) #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Numerical methods in inverse problems #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2402.12752

openalex publication_date 2024/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main results of this paper provide VMO-type estimates for the quadratic tilt-excess on varifolds with critical generalized mean curvature. These estimates apply to varifolds with "almost-integral" density which are close to a multiplicity one m-disc in a ball in the usual senses. The class of almost-integral varifolds allows for varifolds with non-perpendicular mean curvature. Moreover, the estimates hold uniformly for every point in a relatively open set in spt||V|| and naturally imply a Reifenberg-type parametrization. The proof relies upon generalizing the Q-valued Lipschitz approximation and Sobolev-Poincaré estimates of arXiv:0808.3660 to almost-integral rectifiable varifolds.

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