Fine Properties of Sets of Finite Perimeter in Doubling Metric Measure Spaces

By Luigi Ambrosio. 2002

200 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/656427645259b3f23e7d84ee12ef4dd0e38c3027

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Citations in the corpus

Rectifiability of the reduced boundary for sets of finite perimeter over $\RCD(K,N)$ spaces. (2019, background): “6 ELIA BRUÈ, ENRICO PASQUALETTO, AND DANIELE SEMOLA Dropping the global integrability condition on f = χE , let us recall now the analogous definition of set of finite perimeter in a metric measure space (see again [1, 41, 3]).”
Rectifiability of Sets of Finite Perimeter in Carnot Groups: Existence of a Tangent Hyperplane (2008, background): “The non-locality appears also in our argument: indeed, the proof of (4.10) depends on the sign condition of Adexp(tX2)(X1)1E with t arbitrarily large, and this is the right translate, by exp(tX2), of X11E .”
Pointwise properties of functions of bounded variation in metric spaces (2014, unknown): “For the proof, we refer to [1] and [3].”
Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates (2018, unknown): “Example 2.10 Examples of strictly local Dirichlet spaces (X , μ, E,F) that satisfy the volume doubling property and support the 2-Poincaré inequality include: • Complete Riemannian manifolds with non-negative Ricci curvature or more generally RCD(0, N ) spaces in the sense of Ambrosio et al. [10]; •”
Gradient estimates for heat kernels and harmonic functions (2017, background): “Here we are interested in the non-trivial range p ∈ [1, 2).”
The globalization theorem for the Curvature-Dimension condition (2016, background): “as ∈ φs(es(G)) the measure mas is absolutely continuous with respect to the Hausdorff measure of codimension one (see [1] for more details).”
The BV-capacity in metric spaces (2010, background): “The theory of BV-functions in metric measure spaces, see [24, 1, 2], with results like coarea formula and lower semicontinuity of the variation measure play an essential role in our approach.”
A notion of rectifiability modeled on Carnot groups (2000, background): “In recent years, there has been significant interest and progress in the study of rectifiable sets not only in Euclidean space but in more general metric spaces as well (see, for example, [Amb], [AK99b], [AK99a], [Che99], [DS97], [FSSC95], [FSSC99], [GN96], [Kir94], [Mag01], [Pan89], [Whi98].”