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The Regularity of Parametrized Integer Stationary Varifolds in Two Dimensions

Communications on Pure and Applied Mathematics, ISSN: 1097-0312, Vol: 73, Issue: 9, Page: 1981-2042
2020
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We establish an optimal regularity result for parametrized two-dimensional stationary varifolds. Namely, we show that the parametrization map is a smooth minimal branched immersion and that the multiplicity function is constant. We provide some applications of this regularity result, especially in the calculus of variations for the area functional. © 2020 Wiley Periodicals LLC.

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