Geometry of measures in \(R^ n:\) Distribution, rectifiability, and densities
From MaRDI portal
Publication:581576
DOI10.2307/1971410zbMath0627.28008OpenAlexW2318237205WikidataQ29038989 ScholiaQ29038989MaRDI QIDQ581576
Publication date: 1987
Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/1971410
Related Items
Concentrated monotone measures with non-unique tangential behavior in ℝ3, Lower semicontinuity and Young measures in BV without Alberti's Rank-One Theorem, Tangent measures of non-doubling measures, Rectifiable measures, square functions involving densities, and the Cauchy transform, Projections and slices of measures, LOCAL SET APPROXIMATION: MATTILA–VUORINEN TYPE SETS, REIFENBERG TYPE SETS, AND TANGENT SETS, Unnamed Item, UNIFORM ESTIMATES AND BLOW-UP ANALYSIS FOR THE EMDEN EXPONENTIAL EQUATION IN ANY DIMENSION, Partial regularity of harmonic maps from a Riemannian manifold into a Lorentzian manifold, Wasserstein distance and the rectifiability of doubling measures. I, Global Existence of Weak Solutions of the Nematic Liquid Crystal Flow in Dimension Three, Some stationary weak solutions to inhomogeneous Landau-Lifshitz equations in three dimensions, Marstrand's density theorem in the Heisenberg group, Dynamics of the scenery flow and conical density theorems, Unnamed Item, A-free measures and applications, Rigidity and stability of submanifolds with entropy close to one, On rectifiable measures in Carnot groups: representation, Order‐two density of sets and measures with non‐integral dimension, Uniform measures and uniform rectifiability, The weak lower density condition and uniform rectifiability, Parabolic rectifiability, tangent planes and tangent measures, On sets with unit Hausdorff density in homogeneous groups, Microlocal analysis of singular measures, Uhlenbeck compactness for Yang-Mills flow in higher dimensions, LOCAL GEOMETRY OF SELF-SIMILAR SETS: TYPICAL BALLS, TANGENT MEASURES AND ASYMPTOTIC SPECTRA, On the upper regularity dimensions of measures, Self-affine sets with fibred tangents, Marstrand-Mattila rectifiability criterion for 1-codimensional measures in Carnot groups, Minimization of Anisotropic Energies in Classes of Rectifiable Varifolds, Singularities of harmonic maps, On finite configurations in the spectra of singular measures, The packing dimension of projections and sections of measures, On Serrin’s overdetermined problem and a conjecture of Berestycki, Caffarelli and Nirenberg, Characterization of rectifiable measures in terms of 𝛼-numbers, Soap film spanning an elastic link, Uniformly distributed measures have big pieces of Lipschitz graphs locally, Order‐two density and the strong law of large numbers, A Marstrand theorem for measures with polytope density, The Variations of Yang–Mills Lagrangian, Generalized Multiscale Young Measures, The boundedness of Riesz 𝑠-transforms of measures in ℝⁿ, Unnamed Item, Tangent Halfspaces to Sets of Finite Perimeter in Carnot Groups, Partial regularity for stationary harmonic maps at a free boundary, Variationally harmonic maps with general boundary conditions: boundary regularity, Square functions and uniform rectifiability, Lower semicontinuity of multiple µ-quasiconvex integrals, Two sufficient conditions for rectifiable measures, Singular points of Hölder asymptotically optimally doubling measures, An elementary approach to the dimension of measures satisfying a first-order linear PDE constraint, Scenery Flow, Conical Densities, and Rectifiability, Boundary structure and size in terms of interior and exterior harmonic measures in higher dimensions, Regularity and Blow-Up Analysis for J-Holomorphic Maps, Local conical dimensions for measures, Structure of distributions generated by the scenery flow, Dynamics of the scenery flow and geometry of measures, Reflectionless Measures and the Mattila-Melnikov-Verdera Uniform Rectifiability Theorem, Endpoint Fourier restriction and unrectifiability, Relative multifractal box-dimensions, Plateau's Problem as a Singular Limit of Capillarity Problems, Some results about the regularities of multifractal measures, On some notions of tangent space to a measure, LIMITS OF SOLUTIONS TO THE GENERALIZED GINZBURG-LANDAU FUNCTIONAL, Tangent fields, intrinsic stationarity, and self similarity, Eigenvalues of singular measures and Connes' noncommutative integration, The Huovinen transform and rectifiability of measures, Structure of sets which are well approximated by zero sets of harmonic polynomials, On the singular part of measures constrained by linear PDEs and applications, On rectifiable measures in Carnot groups: Marstrand-Mattila rectifiability criterion, Fine properties of functions of bounded deformation -- an approach via linear PDEs, Tangent lines and Lipschitz differentiability spaces, Generalized rectifiability of measures and the identification problem, The singular set of mean curvature flow with generic singularities, Solution manifold and its statistical applications, Motion of concentration sets in Ginzburg-Landau equations., A study of measure-theoretic area formulas, Non existence of quasi-harmonic spheres, Concentration sets of the Landau-Lifshitz system and quasi-mean curvature flows, Conical \(3\)-uniform measures: a family of new examples and characterizations, Existence of solutions to a general geometric elliptic variational problem, Michell truss type theories as a \(\Gamma\)-limit of optimal design in linear elasticity, On the structure of \({\mathcal A}\)-free measures and applications, On sets minimizing their weighted length in uniformly convex separable Banach spaces, Cones, rectifiability, and singular integral operators, On rectifiable measures in Carnot groups: existence of density, On Bandt's tangential distribution for self-similar measures, Lower semicontinuity and relaxation of signed functionals with linear growth in the context of \(\mathcal A\)-quasiconvexity, Reflectionless measures for Calderón-Zygmund operators. I: General theory, A sufficient condition for mobile sampling in terms of surface density, Wasserstein distance and the rectifiability of doubling measures. II, A sharp bound on the Hausdorff dimension of the singular set of a uniform measure, Random cutout sets with spatially inhomogeneous intensities, Singular integrals, analytic capacity and rectifiability, Flatness of domains and doubling properties of measures supported on their boundary, with applications to harmonic measure, Measuring human activity spaces from GPS data with density ranking and summary curves, Geometry of measures in real dimensions via Hölder parameterizations, Lipschitz functions with prescribed blowups at many points, A direct approach to Plateau's problem in any codimension, Homogenization of functionals with linear growth in the context of \(\mathcal A\)-quasiconvexity, Singular integrals on Ahlfors-David regular subsets of the Heisenberg group, Calderón-Zygmund capacities and Wolff potentials on Cantor sets, Regularities of general Hausdorff and packing functions, Absolute continuity of harmonic measure for domains with lower regular boundaries, Partial regularity of a minimizer of the relaxed energy for biharmonic maps, Reflectionless measures for Calderón-Zygmund operators. II: Wolff potentials and rectifiability, Scaling scenery of \((\times m, \times n)\) invariant measures, Unrectifiable 1-sets with moderate essential flatness satisfy Besicovitch's \(\frac 12\)-conjecture, On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1, Harmonic functions on metric measure spaces, A direct approach to the anisotropic Plateau problem, Regularities of multifractal measures, Solutions to the Reifenberg plateau problem with cohomological spanning conditions, Existence results for minimizers of parametric elliptic functionals, Line defects in the small elastic constant limit of a three-dimensional Landau-de Gennes model, Limiting motion for the parabolic Ginzburg-Landau equation with infinite energy data, Multiscale analysis of 1-rectifiable measures. II: Characterizations, Uniform rectifiability from mean curvature bounds, Regularity of the singular set in a two-phase problem for harmonic measure with Hölder data, Small local action of singular integrals on spaces of non-homogeneous type, On a fractional Ginzburg-Landau equation and 1/2-harmonic maps into spheres, On the \(\frac 12\)-problem of Besicovitch: quasi-arcs do not contain sharp saw-teeth, On the strong regularity with the multifractal measures in a probability space, A direct approach to Plateau's problem, Asymptotical behaviour of the Yang-Mills flow and singular Yang-Mills connections, Caloric measure in parabolic flat domains, Locality of the perimeter in Carnot groups and chain rule, A removal singularity theorem of the Donaldson-Thomas instanton on compact Kähler threefolds, Rectifiability of sets of finite perimeter in Carnot groups: existence of a tangent hyperplane, Lower semicontinuity for integral functionals in the space of functions of bounded deformation via rigidity and Young measures, Riesz s-equilibrium measures on \(d\)-dimensional fractal sets as \(s\) approaches \(d\), Tangent measures of elliptic measure and applications, Asymptotics for the Ginzburg-Landau equation on manifolds with boundary under homogeneous Neumann condition, Comparing homologies: Čech's theory, singular chains, integral flat chains and integral currents, Multifractal geometry of slices of measures, \( \Omega \)-symmetric measures and related singular integrals, On uniform measures in the Heisenberg group, Blow-ups of caloric measure in time varying domains and applications to two-phase problems, Characterisation of upper gradients on the weighted Euclidean space and applications, Some results on Sobolev spaces with respect to a measure and applications to a new transport problem, Characterization of generalized Young measures generated by \({\mathcal{A}} \)-free measures, On the smoothness of Hölder doubling measures, Symmetry properties of average densities and tangent measure distributions of measures on the line, Generalized cluster trees and singular measures, Tangent measure distributions of hyperbolic Cantor sets, Gradient of the single layer potential and quantitative rectifiability for general Radon measures, Rigidity of the 1-Bakry-Émery inequality and sets of finite Perimeter in RCD spaces, The blow-up locus of heat flows for harmonic maps, Geometry of \(1\)-codimensional measures in Heisenberg groups, Mapping problems, fundamental groups and defect measures, The multifractal spectra of projected measures in Euclidean spaces, The structure of \(\mathcal{A}\)-free measures revisited, Regularity of Dirac-harmonic maps with \(\lambda\)-curvature term in higher dimensions, Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints, On dimension and regularity of vector-valued measures under Fourier analytic constraints, Sampling trajectories for the short-time Fourier transform, \(L^p(\mu)\)-estimation of tangent maps, Multiscale analysis of 1-rectifiable measures: necessary conditions, Characterising rectifiable metric spaces using tangent spaces, Dimension estimates for vectorial measures with restricted spectrum, Lectures on dynamics, fractal geometry, and metric number theory, Tangents and rectifiability of Ahlfors regular Lipschitz differentiability spaces, Nearly flat almost monotone measures are big pieces of Lipschitz graphs, The Lip-lip equality is stable under blow-up
