Reconstructions of distances by energy forms

Ohta, Shin-ichi

doi:10.1090/S0002-9939-06-08354-7

Reconstructions of distances by energy forms
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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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