Currents in metric spaces

DOI10.1007/BF02392711zbMath0984.49025OpenAlexW2018294758MaRDI QIDQ5926357

Publication date: 14 May 2002

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02392711

zbMATH Keywords

Euclidean isoperimetric inequality generalized Plateau problem metric spaces normal currents rectifiable currents

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Geometric measure and integration theory, integral and normal currents in optimization (49Q15)

Related Items (only showing first 100 items - show all)

Intrinsic regular hypersurfaces in Heisenberg groups ⋮ Morse quasiflats. I ⋮ The structure of minimal surfaces in \(\mathrm{CAT}(0)\) spaces ⋮ On the singular part of measures constrained by linear PDEs and applications ⋮ Area minimizing surfaces of bounded genus in metric spaces ⋮ Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1-Poincaré inequality ⋮ On diameter controls and smooth convergence away from singularities ⋮ Intrinsic regular submanifolds in Heisenberg groups are differentiable graphs ⋮ Rigidity of the Pu inequality and quadratic isoperimetric constants of normed spaces ⋮ Some applications of metric currents to complex analysis ⋮ The tetrahedral property and a new Gromov-Hausdorff compactness theorem ⋮ Infinitesimal structure of differentiability spaces, and metric differentiation ⋮ Intrinsic flat convergence of covering spaces ⋮ Metric currents and Alberti representations ⋮ On the structure of flat chains modulo \(p\) ⋮ On the structure of \({\mathcal A}\)-free measures and applications ⋮ On sets minimizing their weighted length in uniformly convex separable Banach spaces ⋮ Flat convergence for integral currents in metric spaces ⋮ Three superposition principles: currents, continuity equations and curves of measures ⋮ Weak and strong convergence of derivations and stability of flows with respect to MGH convergence ⋮ Intrinsic flat stability of the positive mass theorem for graphical hypersurfaces of Euclidean space ⋮ Metric currents and polylipschitz forms ⋮ Regular submanifolds, graphs and area formula in Heisenberg groups ⋮ Metric cycles, curves and solenoids ⋮ An upper gradient approach to weakly differentiable cochains ⋮ Hypersurfaces and variational formulas in sub-Riemannian Carnot groups ⋮ Dehn functions and Hölder extensions in asymptotic cones ⋮ Integration of Hölder forms and currents in snowflake spaces ⋮ Some remarks on the distributional Jacobian ⋮ Ricci curvature and orientability ⋮ A primer on Carnot groups: homogenous groups, Carnot-Carathéodory spaces, and regularity of their isometries ⋮ Near-equality of the Penrose inequality for rotationally symmetric Riemannian manifolds ⋮ An ultrametricity condition for pretangent spaces ⋮ Stability of graphical tori with almost nonnegative scalar curvature ⋮ Partial regularity for mass-minimizing currents in Hilbert spaces ⋮ Intrinsic flat continuity of Ricci flow through neckpinch singularities ⋮ Metric currents and geometry of Wasserstein spaces ⋮ Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type ⋮ Compactness for manifolds and integral currents with bounded diameter and volume ⋮ Almost rigidity of the positive mass theorem for asymptotically hyperbolic manifolds with spherical symmetry ⋮ Hilbert volume in metric spaces. I ⋮ The Monge problem for distance cost in geodesic spaces ⋮ On the structure of finite perimeter sets in step 2 Carnot groups ⋮ Flat chains of finite size in metric spaces ⋮ Relating notions of convergence in geometric analysis ⋮ Flat forms in Banach spaces ⋮ Sewing Riemannian manifolds with positive scalar curvature ⋮ Differentiability of intrinsic Lipschitz functions within Heisenberg groups ⋮ Regularity of area minimizing currents mod \(p\) ⋮ Lipschitz connectivity and filling invariants in solvable groups and buildings. ⋮ Weak closure of singular Abelian \(L ^{p }\)-bundles in 3 dimensions ⋮ Metric currents and the Poincaré inequality ⋮ Inverse function theorems and Jacobians over metric spaces ⋮ Differentiability and approximate differentiability for intrinsic Lipschitz functions in Carnot groups and a Rademacher theorem ⋮ Regularity of area minimizing currents I: gradient \(L^p\) estimates ⋮ Geodesic manifolds with a transitive subset of smooth biLipschitz maps ⋮ Some basic theorems on flat \(G\) chains ⋮ Non compact boundaries of complex analytic varieties in Hilbert spaces ⋮ Gamma limit of the nonself-dual Chern-Simons-Higgs energy ⋮ Flat chains in Banach spaces ⋮ On weak super Ricci flow through neckpinch ⋮ Integrable boundaries and fractals for Hölder classes; the Gauss-Green theorem ⋮ Area minimizing discs in metric spaces ⋮ Lusin-type approximation of Sobolev by Lipschitz functions, in Gaussian and \(\mathrm{RCD}(K,\infty)\) spaces ⋮ Sub-Riemannian vs. Euclidean dimension comparison and fractal geometry on Carnot groups ⋮ Metric betweenness, Ptolemaic spaces, and isometric embeddings of pretangent spaces in \(\mathbb R\) ⋮ Notes on a slice distance for singular \(L^p\)-bundles ⋮ Ultrametricity and metric betweenness in tangent spaces to metric spaces ⋮ Decomposition of acyclic normal currents in a metric space ⋮ On conditions for unrectifiability of a metric space ⋮ Rectifiability of flat chains in Banach spaces with coefficients in \(\mathbb Z_p\) ⋮ The nonlinear stability of rotationally symmetric spaces with low regularity ⋮ Sub-Riemannian calculus and monotonicity of the perimeter for graphical strips ⋮ The resolution of the Yang-Mills plateau problem in super-critical dimensions ⋮ Local currents in metric spaces ⋮ Fractures and vector valued maps ⋮ Weak convergence of currents and cancellation ⋮ Filling invariants of stratified nilpotent Lie groups ⋮ Gromov-Hausdorff convergence of non-Archimedean fuzzy metric spaces ⋮ A generalized tetrahedral property ⋮ An intrinsic flat limit of Riemannian manifolds with no geodesics ⋮ Volumes and limits of manifolds with Ricci curvature and mean curvature bounds ⋮ A continuous model of transportation revisited ⋮ Lower semicontinuity of ADM mass under intrinsic flat convergence ⋮ Semicontinuity of eigenvalues under intrinsic flat convergence ⋮ Pull-back of metric currents and homological boundedness of BLD-elliptic spaces ⋮ Infinitesimal hilbertianity of locally \(\mathrm{CAT}(\kappa)\)-spaces ⋮ Optimal isoperimetric inequalities for surfaces in any codimension in Cartan-Hadamard manifolds ⋮ Sobolev bounds and convergence of Riemannian manifolds ⋮ The coincidence of the homologies of integral currents and of integral singular chains, via cosheaves ⋮ Functions of bounded fractional variation and fractal currents ⋮ A differentiable structure for metric measure spaces ⋮ A product-estimate for Ginzburg-Landau and corollaries ⋮ Decomposition of integral metric currents ⋮ Higher rank hyperbolicity ⋮ Lipschitz chain approximation of metric integral currents ⋮ Some results on maps that factor through a tree ⋮ On some infinite sums of integer valued Dirac's masses ⋮ Lorentzian area and volume estimates for integral mean curvature bounds ⋮ BV functions and sets of finite perimeter in sub-Riemannian manifolds

Cites Work

This page was built for publication: Currents in metric spaces