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March 2022 The singular set of minimal surfaces near polyhedral cones
Maria Colombo, Nick Edelen, Luca Spolaor
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J. Differential Geom. 120(3): 411-503 (March 2022). DOI: 10.4310/jdg/1649953512

Abstract

We adapt the method of Simon [26] to prove a $C^{1,\alpha}$-regularity theorem for minimal varifolds which resemble a cone $\mathbf{C}^2_0$ over an equiangular geodesic net. For varifold classes admitting a “no-hole” condition on the singular set, we additionally establish $C^{1,\alpha}$-regularity near the cone $\mathbf{C}^2_0 \times \mathbb{R}^m$. Combined with work of Allard [2], Simon [26], Taylor [29], and Naber–Valtorta [21], our result implies a $C^{1,\alpha}$-structure for the top three strata of minimizing clusters and size-minimizing currents, and a Lipschitz structure on the $(n-3)$-stratum.

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Maria Colombo. Nick Edelen. Luca Spolaor. "The singular set of minimal surfaces near polyhedral cones." J. Differential Geom. 120 (3) 411 - 503, March 2022. https://doi.org/10.4310/jdg/1649953512

Information

Received: 11 December 2017; Accepted: 6 December 2019; Published: March 2022
First available in Project Euclid: 15 April 2022

Digital Object Identifier: 10.4310/jdg/1649953512

Rights: Copyright © 2022 Lehigh University

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Vol.120 • No. 3 • March 2022
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