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Rectifiability and upper Minkowski bounds for singularities of harmonic $Q$-valued maps


De Lellis, Camillo; Marchese, Andrea; Spadaro, Emanuele; Valtorta, Daniele (2018). Rectifiability and upper Minkowski bounds for singularities of harmonic $Q$-valued maps. Commentarii Mathematici Helvetici (CMH), 93(4):737-779.

Abstract

In this article we prove that the singular set of Dirichlet-minimizing $Q$-valued functions is countably $(m−2)$-rectifiable and we give upper bounds for the $(m–2)$-dimensional Minkowski content of the set of singular points with multiplicity $Q$.

Abstract

In this article we prove that the singular set of Dirichlet-minimizing $Q$-valued functions is countably $(m−2)$-rectifiable and we give upper bounds for the $(m–2)$-dimensional Minkowski content of the set of singular points with multiplicity $Q$.

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Additional indexing

Item Type:Journal Article, not_refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:General Mathematics
Language:English
Date:20 November 2018
Deposited On:17 Jan 2019 11:01
Last Modified:25 Sep 2019 00:01
Publisher:European Mathematical Society
ISSN:0010-2571
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.4171/cmh/449

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