Rectifiability and upper Minkowski bounds for singularities of harmonic Q-valued maps
Camillo de Lellis, Andrea Marchese, Emanuele Spadaro, Daniele, Valtorta
TL;DR
This paper proves that the singular set of Dirichlet-minimizing Q-valued functions is countably (m-2)-rectifiable and provides upper bounds for its Minkowski content, advancing understanding of singularities in harmonic Q-valued maps.
Contribution
It establishes rectifiability and Minkowski bounds for singularities of harmonic Q-valued maps, a novel geometric measure theory result.
Findings
Singular set is countably (m-2)-rectifiable.
Upper bounds for Minkowski content of singularities.
Enhanced understanding of the structure of singularities.
Abstract
In this article we prove that the singular set of Dirichlet-minimizing -valued functions is countably -rectifiable and we give upper bounds for the -dimensional Minkowski content of the set of singular points with multiplicity .
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