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

Philippe Logaritsch and Andrea Marchese

Contact the author: Please use for correspondence this email.
Submission date: 24. Mar. 2014 (revised version: March 2014)
Pages: 6
published in: Archiv der Mathematik, 102 (2014) 5, p. 455-458 
DOI number (of the published article): 10.1007/s00013-014-0642-4
Bibtex
MSC-Numbers: 54C20, 49Q20
Keywords and phrases: Kirszbraun's extension theorem, multiple valued functions, geometric measure theory
Download full preprint: PDF (103 kB)

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