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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


The space of functions of bounded variation on curves in metric measure spaces
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by O. Martio PDF
Conform. Geom. Dyn. 20 (2016), 81-96 Request permission


The approximation modulus, $AM$–modulus for short, was defined in an earlier paper by the author. In this paper it is shown that an $L^1(X)$–function $u$ in a metric measure space $(X,d,\nu )$ can be defined to be of bounded variation on $AM$–a.e. curve in $X$ without an approximation of $u$ by Lipschitz or Newtonian functions. The essential variation of $u$ on $AM$ almost every curve is bounded by a sequence of non-negative Borel functions in $L^1(X)$. The space of such functions is a Banach space and there is a Borel measure associated with $u$. For $X = \mathbf {R}^n$ this gives the classical space of BV functions.
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Additional Information
  • O. Martio
  • Affiliation: Department of Mathematics and Statistics, FI–00014 University of Helsinki, Finland
  • MR Author ID: 120710
  • Email:
  • Received by editor(s): September 24, 2015
  • Received by editor(s) in revised form: February 10, 2016
  • Published electronically: April 19, 2016

  • Dedicated: Dedicated to Jan Malý on his $60^{th}$ birthday
  • © Copyright 2016 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 20 (2016), 81-96
  • MSC (2010): Primary 26A45; Secondary 26B30, 30L99
  • DOI:
  • MathSciNet review: 3488026