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Reconstructions of distances by energy forms
Author(s):
Shin-ichi
Ohta
Journal:
Proc. Amer. Math. Soc.
134
(2006),
3405-3415.
MSC (2000):
Primary 58C05, 53C60
Posted:
May 8, 2006
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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:
10.1090/S0002-9939-06-08354-7
PII:
S 0002-9939(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
Posted:
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 of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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