Reconstructions of distances by energy forms
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- by Shin-ichi Ohta PDF
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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.References
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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