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Proceedings of the American Mathematical Society

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

 

 

Reconstructions of distances by energy forms


Author: Shin-ichi Ohta
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
Published electronically: May 8, 2006
MathSciNet review: 2231926
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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

DOI: https://doi.org/10.1090/S0002-9939-06-08354-7
Keywords: Intrinsic distance, Cheeger-type energy form, Korevaar-Schoen-type energy form, strong doubling condition, geodesic bicombing
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
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.