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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Reconstructions of distances by energy forms
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by Shin-ichi Ohta PDF
Proc. Amer. Math. Soc. 134 (2006), 3405-3415 Request permission

Abstract:

We prove that, if a metric measure space admits a stratification so that each stratum satisfies the strong doubling condition, then the intrinsic distance induced from the Cheeger-type energy form coincides with the original distance. In other words, we can reconstruct the distance function by the Cheeger-type energy form. We also observe that this reconstruction does not work for the Korevaar-Schoen-type energy form.
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Additional Information
  • Shin-ichi Ohta
  • Affiliation: Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan
  • Email: sohta@math.kyoto-u.ac.jp
  • Received by editor(s): November 17, 2004
  • Received by editor(s) in revised form: May 25, 2005
  • Published electronically: May 8, 2006
  • Additional Notes: This work was partially supported by the Grant-in-Aid for Scientific Research for Young Scientists (B) 16740034 from the Ministry of Education, Culture, Sports, Science and Technology, Japan.
  • Communicated by: Richard A. Wentworth
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 3405-3415
  • MSC (2000): Primary 58C05, 53C60
  • DOI: https://doi.org/10.1090/S0002-9939-06-08354-7
  • MathSciNet review: 2231926