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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
91/2014

Improved estimate of the singular set of Dir-minimizing Q-valued functions

Matteo Focardi, Andrea Marchese and Emanuele Spadaro

Abstract

In this note we give an estimate of the Minkowski dimension of the set of higher multiplicity points of Almgren's Dir-minimizing multiple valued functions, thus improving the previously known estimate of the Hausdorff dimension.

Received:
Sep 3, 2014
Published:
Sep 11, 2014
MSC Codes:
49Q15, 49Q05, 49N60
Keywords:
Q-valued Functions, Quantitative Strati cation, Area Minimizing Currents

Related publications

inJournal
2015 Repository Open Access
Matteo Focardi, Andrea Marchese and Emanuele Spadaro

Improved estimate of the singular set of Dir-minimizing Q-valued functions via an abstract regularity result

In: Journal of functional analysis, 268 (2015) 11, pp. 3290-3325