Rectifiable-Reifenberg and the regularity of stationary and minimizing harmonic maps
From MaRDI portal
Publication:509693
DOI10.4007/annals.2017.185.1.3zbMath1393.58009arXiv1504.02043OpenAlexW1528923274MaRDI QIDQ509693
Publication date: 17 February 2017
Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1504.02043
Related Items
Generalized rectifiability of measures and the identification problem ⋮ Boundary regularity and stability for spaces with Ricci bounded below ⋮ The singular set of minimal surfaces near polyhedral cones ⋮ Rectifiability of the singular set of harmonic maps into buildings ⋮ Boundary unique continuation on \(C^1\)-dini domains and the size of the singular set ⋮ Global estimates and energy identities for elliptic systems with antisymmetric potentials ⋮ The local structure of the free boundary in the fractional obstacle problem ⋮ Rectifiability of singular sets of noncollapsed limit spaces with Ricci curvature bounded below ⋮ Regularity of the free boundary for the vectorial Bernoulli problem ⋮ Defects of liquid crystals with variable degree of orientation ⋮ Unique continuation on convex domains ⋮ How a minimal surface leaves a thin obstacle ⋮ Energy identity for stationary Yang Mills ⋮ Subsets of rectifiable curves in Banach spaces. I: Sharp exponents in traveling salesman theorems ⋮ The regularity theory for the area functional (in geometric measure theory) ⋮ One-phase free-boundary problems with degeneracy ⋮ Unique Continuation at the Boundary for Harmonic Functions in C1 Domains and Lipschitz Domains with Small Constant ⋮ Rectifiability of line defects in liquid crystals with variable degree of orientation ⋮ Discrete Reifenberg-type theorem ⋮ Boundary regularity of stationary critical points for a Cosserat energy functional ⋮ Uniqueness of some cylindrical tangent cones to special Lagrangians ⋮ An analyst's traveling salesman theorem for sets of dimension larger than one ⋮ The singular structure and regularity of stationary varifolds ⋮ \(L^2\) curvature bounds on manifolds with bounded Ricci curvature ⋮ Quantitative stratification for some free-boundary problems ⋮ Almost everywhere uniqueness of blow-up limits for the lower dimensional obstacle problem ⋮ Multiscale analysis of 1-rectifiable measures. II: Characterizations ⋮ Cheeger \(N\)-clusters ⋮ Regularity of the singular set in a two-phase problem for harmonic measure with Hölder data ⋮ Rectifiability and upper Minkowski bounds for singularities of harmonic \(Q\)-valued maps ⋮ Boundary regularity of mass-minimizing integral currents and a question of Almgren ⋮ Some regularity results for \(p\)-harmonic mappings between Riemannian manifolds ⋮ On the measure and the structure of the free boundary of the lower dimensional obstacle problem ⋮ A note on the singular set of area-minimizing hypersurfaces ⋮ Energy quantization of Willmore surfaces at the boundary of the moduli space ⋮ Quantitative stratification of stationary connections ⋮ Convex functionals and the stratification of the singular set of their stationary points ⋮ Stratification for the singular set of approximate harmonic maps ⋮ On Hölder regularity of the singular set of energy minimizing harmonic maps into closed manifolds ⋮ A proof of Carleson's \(\varepsilon^2\)-conjecture ⋮ Nodal sets of smooth functions with finite vanishing order and \(p\)-sweepouts ⋮ Quantitative regularity for \(p\)-minimizing maps through a Reifenberg theorem ⋮ Effective Reifenberg theorems in Hilbert and Banach spaces ⋮ The thin obstacle problem: a survey ⋮ The Gaussian double-bubble and multi-bubble conjectures ⋮ A remark on two notions of flatness for sets in the Euclidean space ⋮ Regularity of Dirac-harmonic maps with \(\lambda\)-curvature term in higher dimensions ⋮ Rectifiability of the singular set of multiple-valued energy minimizing harmonic maps ⋮ Existence and regularity of optimal shapes for elliptic operators with drift ⋮ Boundary regularity for manifold constrained p(x)‐harmonic maps
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Improved estimate of the singular set of Dir-minimizing \(Q\)-valued functions via an abstract regularity result
- The singular set of an energy minimizing map from \(B^ 4\) to \(S^ 2\)
- Solution of the Plateau problem for \(m\)-dimensional surfaces of varying topological type
- Quantitative stratification and higher regularity for biharmonic maps
- Characterization of \(n\)-rectifiability in terms of Jones' square function. II
- Multiple integrals in the calculus of variations
- A regularity theory for harmonic maps
- Gradient estimates and blow-up analysis for stationary harmonic maps
- On the singular set of stationary harmonic maps
- Geometric conditions and existence of bi-Lipschitz parameterizations
- Frequency of Sobolev and quasiconformal dimension distortion
- Lower bounds on Ricci curvature and quantitative behavior of singular sets
- Quantitative stratification and the regularity of harmonic map flow
- Quantitative stratification and the regularity of mean curvature flow
- Stable stationary harmonic maps to spheres
- Sharp estimates on the first eigenvalue of the \(p\)-Laplacian with negative Ricci lower bound
- Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularity structure
- Reifenberg parameterizations for sets with holes
- Minimizing p-harmonic maps into spheres.
- Weakly Differentiable Functions
- Quantitative Stratification and the Regularity of Harmonic Maps and Minimal Currents
- Critical Sets of Elliptic Equations
- Characterization of \(n\)-rectifiability in terms of Jones' square function. I
