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Publication:4001787
zbMath0743.49018MaRDI QIDQ4001787
Publication date: 18 September 1992
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The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups, Uniform rectifiability implies Varopoulos extensions, Generalized rectifiability of measures and the identification problem, Carleson measure estimates and \(\varepsilon\)-approximation for bounded harmonic functions, without Ahlfors regularity assumptions, The traveling salesman theorem in Carnot groups, Boundedness of the square function and rectifiability, High-dimensional Menger-type curvatures. II: \(d\)-separation and a menagerie of curvatures, Wasserstein distance and the rectifiability of doubling measures. I, Vertical perimeter versus horizontal perimeter, Uniform rectifiability from Carleson measure estimates and {\(\epsilon\)}-approximability of bounded harmonic functions, Sets of absolute continuity for harmonic measure in NTA domains, Harmonic measure on locally flat domains, Cones, rectifiability, and singular integral operators, Absolute continuity of the harmonic measure on low dimensional rectifiable sets, Bi-Lipschitz extensions in the plane, Parabolic singular integrals and uniformly rectifiable sets in the parabolic sense, \(A_\infty\) implies NTA for a class of variable coefficient elliptic operators, Singular integrals, analytic capacity and rectifiability, Regularity of \(\mathcal C^1\) and Lipschitz domains in terms of the Beurling transform, The traveling salesman theorem for Jordan curves, A square function involving the center of mass and rectifiability, Coronizations and big pieces in metric spaces, Hölder curves and parameterizations in the Analyst's traveling salesman theorem, Geometry of measures in real dimensions via Hölder parameterizations, On harmonic measure and rectifiability in uniform domains, The two-phase problem for harmonic measure in VMO, Boundedness of the density normalised Jones' square function does not imply 1-rectifiability, Corona decompositions for parabolic uniformly rectifiable sets, Principal values for Riesz transforms and rectifiability, Hybrid linear modeling via local best-fit flats, Smoothness of the Beurling transform in Lipschitz domains, Quantitative nonorientability of embedded cycles, The Morse-Sard theorem for Sobolev spaces in a borderline case, Some Calderón-Zygmund kernels and their relations to Wolff capacities and rectifiability, Calderón-Zygmund kernels and rectifiability in the plane, Green function estimates on complements of low-dimensional uniformly rectifiable sets, Mass transport and uniform rectifiability, \(L^2\)-boundedness of gradients of single layer potentials for elliptic operators with coefficients of Dini mean oscillation-type, The Morse-Sard theorem in \(W^{n,n} (\Omega)\): A simple proof, Harmonic measure and quantitative connectivity: geometric characterization of the \(L^p\)-solvability of the Dirichlet problem, BMO solvability and absolute continuity of harmonic measure, Absolute continuity of harmonic measure for domains with lower regular boundaries, Boundary rectifiability and elliptic operators with \(W^{1, 1}\) coefficients, Estimates for the maximal singular integral in terms of the singular integral: the case of even kernels, Dahlberg's theorem in higher co-dimension, Variation for the Riesz transform and uniform rectifiability, \(l_p\)-recovery of the most significant subspace among multiple subspaces with outliers, \(L^2\)-boundedness of the Cauchy integral operator for continuous measures, Quantitative comparisons of multiscale geometric properties, Multilayer potentials for higher-order systems in rough domains, Singular integrals on regular curves in the Heisenberg group, Geometric and transformational properties of Lipschitz domains, Semmes-Kenig-Toro domains, and other classes of finite perimeter domains, The measures with an associated square function operator bounded in \(L^2\), Symmetry theorems and uniform rectifiability, Multiscale analysis of 1-rectifiable measures. II: Characterizations, A new characterization of chord-arc domains, The weak-\(A_\infty\) property of harmonic and \(p\)-harmonic measures implies uniform rectifiability, Geometric conditions for the \(L^2\)-boundedness of singular integral operators with odd kernels with respect to measures with polynomial growth in \(\mathbb{R}^d\), A parabolic version of corona decompositions, On the regularity of domains satisfying a uniform hour-glass condition and a sharp version of the Hopf-Oleinik boundary point principle, Quasiconformal planes with bi-Lipschitz pieces and extensions of almost affine maps, High-dimensional Menger-type curvatures. I: Geometric multipoles and multiscale inequalities, The traveling salesman problem in the Heisenberg group: Upper bounding curvature, Square functions and uniform rectifiability, Uniform rectifiability and \(\varepsilon\)-approximability of harmonic functions in \(L^p\), A sharp necessary condition for rectifiable curves in metric spaces, Two sufficient conditions for rectifiable measures, Poincaré-type inequalities and finding good parameterizations, Differentiable points of Sierpinski-like sponges, Square functions, nontangential limits, and harmonic measure in codimension larger than 1, \( \Omega \)-symmetric measures and related singular integrals, Uniform rectifiability and elliptic operators satisfying a Carleson measure condition, A proof of Carleson's \(\varepsilon^2\)-conjecture, Geometric conditions and existence of bi-Lipschitz parameterizations, Sufficient condition for rectifiability involving Wasserstein distance \(W_2\), A singular integral approach to a two phase free boundary problem, Plenty of big projections imply big pieces of Lipschitz graphs, Characterizations of countably \(n\)-rectifiable Radon measures by higher-dimensional Menger curvatures, A family of singular integral operators which control the Cauchy transform, Menger curvatures and \(C^{1,\alpha}\) rectifiability of measures, Quantitative affine approximation for UMD targets, Quasiconformal maps in metric spaces with controlled geometry, A new elliptic measure on lower dimensional sets, Quantitative absolute continuity of harmonic measure and the Dirichlet problem: a survey of recent progress, Compactness, or lack thereof, for the harmonic double layer, Gradient of the single layer potential and quantitative rectifiability for general Radon measures, Effective Reifenberg theorems in Hilbert and Banach spaces, Elliptic measures and square function estimates on 1-sided chord-arc domains, The restricted content and the \(d\)-dimensional Analyst's travelling salesman theorem for general sets, Boundary layer methods for Lipschitz domains in Riemannian manifolds, Boundedness of singular integrals on \(C^{1,{\alpha}}\) intrinsic graphs in the Heisenberg group, Finite square function implies integer dimension, Quantitative Fatou theorems and uniform rectifiability, Square function estimates, the BMO Dirichlet problem, and absolute continuity of harmonic measure on lower-dimensional sets, Hardy spaces, singular integrals and the geometry of Euclidean domains of locally finite perimeter, Singular integrals unsuitable for the curvature method whose \(L^2\)-boundedness still implies rectifiability, Geometric branched covers between generalized manifolds, Approximation of Green functions and domains with uniformly rectifiable boundaries of all dimensions, Extensions and corona decompositions of low-dimensional intrinsic Lipschitz graphs in Heisenberg groups, A selective review on Mumford-Shah minimizers, Ensembles quasi-minimaux avec contrainte de volume et rectifiabilité uniforme, Rectifiable measures, square functions involving densities, and the Cauchy transform, 𝐿^{𝑝}-square function estimates on spaces of homogeneous type and on uniformly rectifiable sets, Dynamics of the scenery flow and conical density theorems, Quantitative Rectifiability and Lipschitz Mappings, Uniform measures and uniform rectifiability, The weak lower density condition and uniform rectifiability, Rectifiability and elliptic measures on 1-sided NTA domains with Ahlfors-David regular boundaries, Iterating the Big‐Pieces operator and larger sets, Singular integrals with variable kernels in dyadic settings, Riesz transform and vertical oscillation in the Heisenberg group, Subsets of rectifiable curves in Banach spaces. I: Sharp exponents in traveling salesman theorems, Necessary condition for the L2 boundedness of the Riesz transform on Heisenberg groups, Carleson perturbations for the regularity problem, Composing and decomposing surfaces and functions, Geometric criteria for C1,α$C^{1,\alpha }$‐rectifiability, A Green function characterization of uniformly rectifiable sets of any codimension, A \(d\)-dimensional analyst's travelling salesman theorem for subsets of Hilbert space, An \(\alpha\)-number characterization of \(L^p\) spaces on uniformly rectifiable sets, Square function estimates for the evolutionary \(p\)-Laplace equation, Carleson measure estimates for caloric functions and parabolic uniformly rectifiable sets, A structure theorem for elliptic and parabolic operators with applications to homogenization of operators of Kolmogorov type, \(C^{1,\alpha}\)-rectifiability in low codimension in Heisenberg groups, Sufficient conditions for C^1,α parametrization and rectifiability, Jump formulas for singular integrals and layer potentials on rectifiable sets, $L^p$ estimates for the variation for singular integrals on uniformly rectifiable sets, Quasisymmetric extension on the real line, Conditions quantitatives de rectifiabilité, Perturbations of elliptic operators in 1-sided chord-arc domains. Part II: Non-symmetric operators and Carleson measure estimates, Characterization of rectifiable measures in terms of 𝛼-numbers, $\varepsilon $-approximability of harmonic functions in $L^p$ implies uniform rectifiability, The Poisson integral formula for variable-coefficient elliptic systems in rough domains, Tangent points of lower content d‐regular sets and β numbers, Uniformly distributed measures have big pieces of Lipschitz graphs locally, Semmes surfaces and intrinsic Lipschitz graphs in the Heisenberg group, The Riesz Transform of Codimension Smaller Than One and the Wolff Energy, Dorronsoro's theorem in Heisenberg groups, Perturbations of elliptic operators in 1-sided chord-arc domains. Part I: Small and large perturbation for symmetric operators, The Maximal Singular Integral: Estimates in Terms of the Singular Integral, Quantitative conditions of rectifiability for varifolds, Wild examples of countably rectifiable sets, On big pieces approximations of parabolic hypersurfaces, Pointwise estimates for Stokes systems with BMO coefficients in Reifenberg domains, Radon measures and Lipschitz graphs, Two examples related to conical energies
