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On conditions for unrectifiability of a metric space

Hajłasz, P and Malekzadeh, S (2015) On conditions for unrectifiability of a metric space. Analysis and Geometry in Metric Spaces, 3 (1). 1 - 14.

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Abstract

© 2015 Piotr Hajłasz and Soheil Malekzadeh. We find necessary and sufficient conditions for a Lipschitz map f : E Rk ! X into a metric space to satisfyHk(f (E)) = 0. An interesting feature of our approach is that despite the fact that we are dealing with arbitrary metric spaces, we employ a variant of the classical implicit function theorem. Applications include pure unrectifiability of the Heisenberg groups.


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Details

Item Type: Article
Status: Published
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Hajłasz, P
Malekzadeh, Ssom13@pitt.eduSOM13
Date: 1 January 2015
Date Type: Publication
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Journal or Publication Title: Analysis and Geometry in Metric Spaces
Volume: 3
Number: 1
Page Range: 1 - 14
DOI or Unique Handle: 10.1515/agms-2015-0001
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Refereed: Yes
Date Deposited: 22 May 2015 21:59
Last Modified: 02 Feb 2019 14:55
URI: http://d-scholarship.pitt.edu/id/eprint/24683

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