Some fine properties of sets of finite perimeter in Ahlfors regular metric measure spaces
From MaRDI portal
Publication:5933429
DOI10.1006/aima.2000.1963zbMath1002.28004OpenAlexW2071904195MaRDI QIDQ5933429
Publication date: 5 January 2003
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/aima.2000.1963
Length, area, volume, other geometric measure theory (28A75) Hausdorff and packing measures (28A78) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15)
Related Items (71)
The weighted isoperimetric-type and Sobolev-type inequalities for hypersurfaces in Carnot groups ⋮ Intrinsic regular hypersurfaces in Heisenberg groups ⋮ Energy scaling law for the regular cone ⋮ Nonsmooth calculus ⋮ Isoperimetric sets in spaces with lower bounds on the Ricci curvature ⋮ Isoperimetric inequality from the poisson equation via curvature ⋮ Vertical perimeter versus horizontal perimeter ⋮ Characteristic points, rectifiability and perimeter measure on stratified groups ⋮ The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations ⋮ Functions of bounded variation on ``good metric spaces ⋮ Metric differentiation, monotonicity and maps to \(L^{1}\) ⋮ Hypersurfaces and variational formulas in sub-Riemannian Carnot groups ⋮ Towards a theory of area in homogeneous groups ⋮ The isoperimetric problemviadirect method in noncompact metric measure spaces with lower Ricci bounds ⋮ Coarea inequality for monotone functions on metric surfaces ⋮ Local vector measures ⋮ Constancy of the dimension in codimension one and locality of the unit normal on $\RCD(K,N)$ spaces ⋮ \(\Gamma \)-convergence of variational functionals with boundary terms in Stein manifolds ⋮ Surface measure on, and the local geometry of, sub-Riemannian manifolds ⋮ AM‐modulus and Hausdorff measure of codimension one in metric measure spaces ⋮ A primer on Carnot groups: homogenous groups, Carnot-Carathéodory spaces, and regularity of their isometries ⋮ Calculus and fine properties of functions of bounded variation on RCD spaces ⋮ Monotone sets and local minimizers for the perimeter in Carnot groups ⋮ The bounded variation capacity and Sobolev-type inequalities on Dirichlet spaces ⋮ Compression bounds for Lipschitz maps from the Heisenberg group to \(L_{1}\) ⋮ Subgraphs of BV functions on RCD spaces ⋮ About the general chain rule for functions of bounded variation ⋮ Obstacle problems on \(\mathrm{RCD}(K, N)\) metric measure spaces ⋮ On the structure of finite perimeter sets in step 2 Carnot groups ⋮ BV and Sobolev homeomorphisms between metric measure spaces and the plane ⋮ Intrinsic Lipschitz graphs in Carnot groups of step 2 ⋮ The chain rule and a compactness theorem for \(BV\) functions in the Heisenberg group \(\mathbf H^{n}\) ⋮ An intrinsic measure for submanifolds in stratified groups ⋮ Smooth approximation for intrinsic Lipschitz functions in the Heisenberg group ⋮ Isoperimetric inequality via Lipschitz regularity of Cheeger-harmonic functions ⋮ Decomposition of geodesics in the Wasserstein space and the globalization problem ⋮ Vertical versus horizontal Poincaré inequalities on the Heisenberg group ⋮ A pointwise characterization of functions of bounded variation on metric spaces ⋮ Isoperimetric and stable sets for log-concave perturbations of Gaussian measures ⋮ On estimates for the Besov norms of solutions to 3D subelliptic equations ⋮ Indecomposable sets of finite perimeter in doubling metric measure spaces ⋮ Unnamed Item ⋮ A note on the extension of BV functions in metric measure spaces ⋮ Perimeter as relaxed Minkowski content in metric measure spaces ⋮ Currents in metric spaces ⋮ On gradient bounds for the heat kernel on the Heisenberg group ⋮ The BV-capacity in metric spaces ⋮ Rectifiability of flat chains in Banach spaces with coefficients in \(\mathbb Z_p\) ⋮ Tangent Halfspaces to Sets of Finite Perimeter in Carnot Groups ⋮ Differentiating maps into \(L^1\), and the geometry of BV functions ⋮ Sub-Riemannian calculus and monotonicity of the perimeter for graphical strips ⋮ Comparisons of relative BV-capacities and Sobolev capacity in metric spaces ⋮ Blow-up estimates at horizontal points and applications ⋮ Locality of the perimeter in Carnot groups and chain rule ⋮ Lower semicontinuity of a class of functionals in \(\text{SBV}_H\) ⋮ 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 ⋮ Blow-up of regular submanifolds in Heisenberg groups and applications ⋮ On the isoperimetric problem in the Heisenberg group \(\mathbb H^n\) ⋮ The Gauss-Green theorem in stratified groups ⋮ Sets with constant normal in Carnot groups: properties and examples ⋮ Rough traces of BV functions in 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 ⋮ The Bernstein problem for Lipschitz intrinsic graphs in the Heisenberg group ⋮ Rigidity of the 1-Bakry-Émery inequality and sets of finite Perimeter in RCD spaces ⋮ Fine properties of functions with bounded variation in Carnot-Carathéodory spaces ⋮ The isoperimetric problem for regular and crystalline norms in \({\mathbb{H}}^1\) ⋮ BV functions and sets of finite perimeter in sub-Riemannian manifolds ⋮ On transversal submanifolds and their measure ⋮ Stability and continuity of functions of least gradient
Cites Work
- Nuovi teoremi relativi alle misure \((r - 1)\)-dimensionali in uno spazio ad \(r\) dimensioni
- A new proof of the compactness theorem for integral currents
- Balls and metrics defined by vector fields. I: Basic properties
- Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
- Quasiconformal maps in metric spaces with controlled geometry
- Differentiability of Lipschitz functions on metric measure spaces
- Sobolev and isoperimetric inequalities for degenerate metrics
- On the Poincaré inequality for vector fields
- Rectifiable sets in metric and Banach spaces
- The Poincaré inequality for vector fields satisfying Hörmander's condition
- Sobolev inequalities on homogeneous spaces
- The geometric Sobolev embedding for vector fields and the isoperimetric inequality
- On the nonexistence of bilipschitz parameterizations and geometric problems about \(A_ \infty\)-weights
- Sobolev spaces on an arbitrary metric space
- Ahlfors \(Q\)-regular spaces with arbitrary \(Q>1\) admitting weak Poincaré inequality
- Normal and integral currents
- Su una teoria generale della misura \((r-1)\)-dimensionale in uno spazio ad \(r\) dimensioni
- Sur les ensembles de périmètre fini dans le groupe de heisenberg
- Rectifiable Metric Spaces: Local Structure and Regularity of the Hausdorff Measure
- Sobolev met Poincaré
- A notion of rectifiability modeled on Carnot groups
- [https://portal.mardi4nfdi.de/wiki/Publication:5689214 Isoperimetric and Sobolev inequalities for Carnot-Carath�odory spaces and the existence of minimal surfaces]
- Currents in metric spaces
- Rectifiability and perimeter in the Heisenberg group
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Some fine properties of sets of finite perimeter in Ahlfors regular metric measure spaces