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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
42/2014

Kirszbraun's extension theorem fails for Almgren's multiple valued functions

Philippe Logaritsch and Andrea Marchese

Abstract

We prove that in general it is not possible to extend a Lipschitz multiple valued function without increasing the Lipschitz constant, i.e. we show that there is no analog of Kirszbraun's extension theorem for Almgren's multiple valued functions

Received:
Mar 24, 2014
Published:
Mar 31, 2014
MSC Codes:
54C20, 49Q20
Keywords:
Kirszbraun's extension theorem, multiple valued functions, geometric measure theory

Related publications

inJournal
2014 Repository Open Access
Philippe Logaritsch and Andrea Marchese

Kirszbraun's extension theorem fails for Almgren's multiple valued functions

In: Archiv der Mathematik, 102 (2014) 5, pp. 455-458