Fine properties of sets of finite perimeter in doubling metric measure spaces
From MaRDI portal
Publication:1611756
DOI10.1023/A:1016548402502zbMath1037.28002OpenAlexW147598125MaRDI QIDQ1611756
Publication date: 28 August 2002
Published in: Set-Valued Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1023/a:1016548402502
Contents, measures, outer measures, capacities (28A12) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Length, area, volume, other geometric measure theory (28A75) Sobolev (and similar kinds of) spaces of functions of discrete variables (46E39)
Related Items (94)
The variational 1-capacity and BV functions with zero boundary values on doubling metric spaces ⋮ Isoperimetric sets in spaces with lower bounds on the Ricci curvature ⋮ An analog of the Neumann problem for the 1-Laplace equation in the metric setting: existence, boundary regularity, and stability ⋮ Characteristic points, rectifiability and perimeter measure on stratified groups ⋮ Functional capacities on the Grushin space \({\mathbb {G}}^n_\alpha \) ⋮ The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations ⋮ Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds ⋮ Characterizations of sets of finite perimeter using heat kernels in metric spaces ⋮ A note on BV capacities on Grushin spaces ⋮ Regularity of sets with quasiminimal boundary surfaces in metric spaces ⋮ A Federer-style characterization of sets of finite perimeter on metric spaces ⋮ Metric differentiation, monotonicity and maps to \(L^{1}\) ⋮ The isoperimetric problemviadirect method in noncompact metric measure spaces with lower Ricci bounds ⋮ Pointwise properties of functions of bounded variation in metric spaces ⋮ Brief Survey on Functions of Bounded Variation (BV) in Metric Setting ⋮ Neumann \(p\)-Laplacian problems with a reaction term on metric spaces ⋮ Local vector measures ⋮ Besov class via heat semigroup on Dirichlet spaces. II: BV functions and Gaussian heat kernel estimates ⋮ Constancy of the dimension in codimension one and locality of the unit normal on $\RCD(K,N)$ spaces ⋮ Surface measure on, and the local geometry of, sub-Riemannian manifolds ⋮ A primer on Carnot groups: homogenous groups, Carnot-Carathéodory spaces, and regularity of their isometries ⋮ First-order heat content asymptotics on \(\mathsf{RCD} (K, N)\) spaces ⋮ Calculus and fine properties of functions of bounded variation on RCD spaces ⋮ An ultrametricity condition for pretangent spaces ⋮ The bounded variation capacity and Sobolev-type inequalities on Dirichlet spaces ⋮ Modulus of families of sets of finte perimeter and quasiconformal maps between metric spaces of globally Q-bounded geometry ⋮ Compression bounds for Lipschitz maps from the Heisenberg group to \(L_{1}\) ⋮ The Neumann and Dirichlet problems for the total variation flow in metric measure spaces ⋮ Subgraphs of BV functions on RCD spaces ⋮ About the general chain rule for functions of bounded variation ⋮ Capacitary density and removable sets for Newton-Sobolev functions in metric spaces ⋮ A note on indecomposable sets of finite perimeter ⋮ Obstacle problems on \(\mathrm{RCD}(K, N)\) metric measure spaces ⋮ Non-locality, non-linearity, and existence of solutions to the Dirichlet problem for least gradient functions in metric measure spaces ⋮ The isoperimetric problem on Riemannian manifolds via Gromov–Hausdorff asymptotic analysis ⋮ On the structure of finite perimeter sets in step 2 Carnot groups ⋮ BV and Sobolev homeomorphisms between metric measure spaces and the plane ⋮ Rectifiability of the reduced boundary for sets of finite perimeter over \(\operatorname{RCD} ( K , N )\) spaces ⋮ Strong approximation of sets of finite perimeter in metric spaces ⋮ Approximation of BV by SBV functions in metric spaces ⋮ A sharp Leibniz rule for BV functions in metric spaces ⋮ Trace theorems for functions of bounded variation in metric spaces ⋮ Duality of moduli and quasiconformal mappings in metric spaces ⋮ Federer's characterization of sets of finite perimeter in metric spaces ⋮ Relative isoperimetric inequalities and sufficient conditions for finite perimeter on metric spaces ⋮ Isoperimetric inequality via Lipschitz regularity of Cheeger-harmonic functions ⋮ Capacity \& perimeter from \(\alpha\)-Hermite bounded variation ⋮ The equivalence between pointwise Hardy inequalities and uniform fatness ⋮ Extensions and traces of functions of bounded variation on metric spaces ⋮ Decomposition of geodesics in the Wasserstein space and the globalization problem ⋮ A pointwise characterization of functions of bounded variation on metric spaces ⋮ A characterization of Newtonian functions with zero boundary values ⋮ The globalization theorem for the curvature-dimension condition ⋮ Indecomposable sets of finite perimeter in doubling metric measure spaces ⋮ Fine properties and a notion of quasicontinuity for BV functions on metric spaces ⋮ Capacities and 1-strict subsets in metric spaces ⋮ A note on the extension of BV functions in metric measure spaces ⋮ Asymptotic behavior of $BV$ functions and sets of finite perimeter in metric measure spaces ⋮ Polya-Szego inequality and Dirichlet \(p\)-spectral gap for non-smooth spaces with Ricci curvature bounded below ⋮ A notion of fine continuity for BV functions on metric spaces ⋮ Perimeter as relaxed Minkowski content in metric measure spaces ⋮ Traces of Newtonian-Sobolev, Hajlasz-Sobolev, and BV functions on metric spaces ⋮ Neumann problem for \(p\)-Laplace equation in metric spaces using a variational approach: existence, boundedness, and boundary regularity ⋮ Infinitesimal calculus in metric spaces ⋮ BV capacity on generalized Grushin plane ⋮ Ultrametricity and metric betweenness in tangent spaces to metric spaces ⋮ The BV-capacity in metric spaces ⋮ Tangent Halfspaces to Sets of Finite Perimeter in Carnot Groups ⋮ Differentiating maps into \(L^1\), and the geometry of BV functions ⋮ Isoperimetric inequality in the Grushin plane ⋮ Comparisons of relative BV-capacities and Sobolev capacity in metric spaces ⋮ Strict and pointwise convergence of BV functions in metric spaces ⋮ The De Giorgi measure and an obstacle problem related to minimal surfaces in metric spaces ⋮ Rectifiability of sets of finite perimeter in Carnot groups: existence of a tangent hyperplane ⋮ Notions of Dirichlet problem for functions of least gradient in metric measure spaces ⋮ The Gauss-Green theorem in stratified groups ⋮ Approximation by Hölder functions in Besov and Triebel-Lizorkin spaces ⋮ Discrete convolutions of \(\text{BV}\) functions in quasiopen sets in metric spaces ⋮ Adams inequality on metric measure spaces ⋮ Rough traces of BV functions in metric measure spaces ⋮ Approximation by uniform domains in doubling quasiconvex metric spaces ⋮ Gradient estimates for heat kernels and harmonic functions ⋮ Relaxation and integral representation for functionals of linear growth on metric measure spaces ⋮ A Talenti-type comparison theorem for \(\mathrm{RCD}(K,N)\) spaces and applications ⋮ Semmes family of curves and a characterization of functions of bounded variation in terms of curves ⋮ Boundary measures, generalized Gauss-Green formulas, and mean value property in metric measure spaces ⋮ A new Federer-type characterization of sets of finite perimeter ⋮ Rigidity of the 1-Bakry-Émery inequality and sets of finite Perimeter in RCD spaces ⋮ Local minimizers and gamma-convergence for nonlocal perimeters in Carnot groups ⋮ Domains in metric measure spaces with boundary of positive mean curvature, and the Dirichlet problem for functions of least gradient ⋮ BV functions and sets of finite perimeter in sub-Riemannian manifolds ⋮ On rough traces of BV functions ⋮ On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth ⋮ Stability and continuity of functions of least gradient
This page was built for publication: Fine properties of sets of finite perimeter in doubling metric measure spaces