Reifenberg parameterizations for sets with holes
From MaRDI portal
Publication:3115414
DOI10.1090/S0065-9266-2011-00629-5zbMath1236.28002arXiv0910.4869MaRDI QIDQ3115414
Publication date: 21 February 2012
Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0910.4869
Minimal surfaces and optimization (49Q05) Variational problems in a geometric measure-theoretic setting (49Q20) Length, area, volume, other geometric measure theory (28A75) Optimality conditions (49K99)
Related Items (47)
Structure of sets which are well approximated by zero sets of harmonic polynomials ⋮ Generalized rectifiability of measures and the identification problem ⋮ Boundary unique continuation on \(C^1\)-dini domains and the size of the singular set ⋮ Uniform measures and uniform rectifiability ⋮ Hard Sard: quantitative implicit function and extension theorems for Lipschitz maps ⋮ Hölder curves and parameterizations in the Analyst's traveling salesman theorem ⋮ Geometry of measures in real dimensions via Hölder parameterizations ⋮ Calderón-Zygmund estimates for nonlinear parabolic equations with matrix weights on nonsmooth domains ⋮ Subsets of rectifiable curves in Banach spaces. I: Sharp exponents in traveling salesman theorems ⋮ Characterization of \(n\)-rectifiability in terms of Jones' square function. II ⋮ Geometric criteria for C1,α$C^{1,\alpha }$‐rectifiability ⋮ A \(d\)-dimensional analyst's travelling salesman theorem for subsets of Hilbert space ⋮ Small-constant uniform rectifiability ⋮ Sufficient conditions for C^1,α parametrization and rectifiability ⋮ Global gradient estimates for divergence-type elliptic problems involving general nonlinear operators ⋮ Discrete Reifenberg-type theorem ⋮ An analyst's traveling salesman theorem for sets of dimension larger than one ⋮ Characterization of rectifiable measures in terms of 𝛼-numbers ⋮ The singular structure and regularity of stationary varifolds ⋮ Tangent points of lower content d‐regular sets and β numbers ⋮ Uniformly distributed measures have big pieces of Lipschitz graphs locally ⋮ Dahlberg's theorem in higher co-dimension ⋮ Quantitative comparisons of multiscale geometric properties ⋮ Quasisymmetry and rectifiability of quasispheres ⋮ Quantitative stratification for some free-boundary problems ⋮ Rectifiable-Reifenberg and the regularity of stationary and minimizing harmonic maps ⋮ Multiscale analysis of 1-rectifiable measures. II: Characterizations ⋮ Rectifiability and upper Minkowski bounds for singularities of harmonic \(Q\)-valued maps ⋮ Quasiconformal planes with bi-Lipschitz pieces and extensions of almost affine maps ⋮ On the measure and the structure of the free boundary of the lower dimensional obstacle problem ⋮ Global gradient estimates in weighted Lebesgue spaces for parabolic operators ⋮ Stratification for the singular set of approximate harmonic maps ⋮ Poincaré-type inequalities and finding good parameterizations ⋮ \( \Omega \)-symmetric measures and related singular integrals ⋮ Quantitative regularity for \(p\)-minimizing maps through a Reifenberg theorem ⋮ Sufficient condition for rectifiability involving Wasserstein distance \(W_2\) ⋮ A family of singular integral operators which control the Cauchy transform ⋮ Optimal regularity estimates for general nonlinear parabolic equations ⋮ A new elliptic measure on lower dimensional sets ⋮ Effective Reifenberg theorems in Hilbert and Banach spaces ⋮ Potential estimates of superquadratic elliptic systems with VMO coefficients in Reifenberg domains ⋮ The restricted content and the \(d\)-dimensional Analyst's travelling salesman theorem for general sets ⋮ The dirichlet-conormal problem with homogeneous and inhomogeneous boundary conditions ⋮ A remark on two notions of flatness for sets in the Euclidean space ⋮ Global weighted estimates for nonlinear elliptic obstacle problems over Reifenberg domains ⋮ Rectifiability of the singular set of multiple-valued energy minimizing harmonic maps ⋮ Multiscale analysis of 1-rectifiable measures: necessary conditions
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Solution of the Plateau problem for \(m\)-dimensional surfaces of varying topological type
- Harmonic measure and arclength
- Rectifiable sets and the traveling salesman problem
- Chord-arc surfaces with small constant. I
- Chord-arc surfaces with small constant. II: Good parametrizations
- Morceaux de graphes lipschitziens et intégrales singulières sur une surface
- A generalization of Reifenberg's theorem in \({\mathbb{R}}^3\)
- Quasiconformal maps of cylindrical domains
- Wiggly sets and limit sets
- Menger curvature and rectifiability
- Harmonic measure, \(L^ 2\) estimates and the Schwarzian derivative
- Geometric conditions and existence of bi-Lipschitz parameterizations
- Analytic capacity, rectifiability, Menger curvature and the Cauchy integral
- The Cauchy integral, analytic capacity and subsets of quasicircles
- Uniform rectifiability and singular sets
- An epiperimetric inequality related to the analyticity of minimal surfaces
- On the analyticity of minimal surfaces
- Hypersurfaces in R n Whose Unit Normal has Small BMO Norm
- A Characterization of Potential Spaces
- The planar Schönflies theorem for Lipschitz maps
- Quantitative Rectifiability and Lipschitz Mappings
- Conditions quantitatives de rectifiabilité
- Quantifying curvelike structures of measures by usingL2 Jones quantities
- Hardy spaces, $A_\infty$, and singular integrals on chord-arc domains
This page was built for publication: Reifenberg parameterizations for sets with holes
