Abstract
We construct Sobolev spaces and energy functionals over maps between metric spaces under the strong measure contraction property of Bishop–Gromov type, which is a generalized notion of Ricci curvature bounded below. We also present the notion of generalized measure contraction property, which gives a characterization of energies by approximating energies of Sturm type over Lipschitz maps.
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Kuwae, K., Shioya, T. On Generalized Measure Contraction Property and Energy Functionals over Lipschitz Maps. Potential Analysis 15, 105–121 (2001). https://doi.org/10.1023/A:1011218425271
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DOI: https://doi.org/10.1023/A:1011218425271