On Conditions for Unrectifiability of a Metric Space

Piotr Hajłasz; Soheil Malekzadeh

Analysis and Geometry in Metric Spaces (2015)

  • Volume: 3, Issue: 1, page 1-14, electronic only
  • ISSN: 2299-3274

Abstract

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We find necessary and sufficient conditions for a Lipschitz map f : E ⊂ ℝk → X into a metric space to satisfy ℋk(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.

How to cite

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Piotr Hajłasz, and Soheil Malekzadeh. "On Conditions for Unrectifiability of a Metric Space." Analysis and Geometry in Metric Spaces 3.1 (2015): 1-14, electronic only. <http://eudml.org/doc/268901>.

@article{PiotrHajłasz2015,
abstract = {We find necessary and sufficient conditions for a Lipschitz map f : E ⊂ ℝk → X into a metric space to satisfy ℋk(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.},
author = {Piotr Hajłasz, Soheil Malekzadeh},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {geometric measure theory; unrectifiability; metric spaces; Sard theorem; Carnot-Carathéodory spaces; Carnot-Carathéodory spaces},
language = {eng},
number = {1},
pages = {1-14, electronic only},
title = {On Conditions for Unrectifiability of a Metric Space},
url = {http://eudml.org/doc/268901},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Piotr Hajłasz
AU - Soheil Malekzadeh
TI - On Conditions for Unrectifiability of a Metric Space
JO - Analysis and Geometry in Metric Spaces
PY - 2015
VL - 3
IS - 1
SP - 1
EP - 14, electronic only
AB - We find necessary and sufficient conditions for a Lipschitz map f : E ⊂ ℝk → X into a metric space to satisfy ℋk(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.
LA - eng
KW - geometric measure theory; unrectifiability; metric spaces; Sard theorem; Carnot-Carathéodory spaces; Carnot-Carathéodory spaces
UR - http://eudml.org/doc/268901
ER -

References

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