The authors introduce α-Hermite BV spaces, perimeters, and capacities, and prove that they satisfy coarea, Sobolev, isoperimetric, trace, and isocapacity inequalities, together with an L1 mean-curvature result for a restricted perimeter.
Ambrosio, Fine properties of sets of finite perimeter i n doubling metric measure spaces, Set-V alued and V ariational Analysis 10 (2002), 111-128
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Capacity & Perimeter from $\alpha$-Hermite Bounded Variation
The authors introduce α-Hermite BV spaces, perimeters, and capacities, and prove that they satisfy coarea, Sobolev, isoperimetric, trace, and isocapacity inequalities, together with an L1 mean-curvature result for a restricted perimeter.