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The Regularity of Parametrized Integer Stationary Varifolds in Two Dimensions
Author(s) -
Pigati Alessandro,
Rivière Tristan
Publication year - 2020
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21927
Subject(s) - mathematics , parametrization (atmospheric modeling) , integer (computer science) , constant (computer programming) , immersion (mathematics) , multiplicity (mathematics) , mathematical analysis , pure mathematics , computer science , physics , quantum mechanics , programming language , radiative transfer
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