Solution of the Plateau problem for \(m\)-dimensional surfaces of varying topological type
From MaRDI portal
Publication:773798
DOI10.1007/BF02547186zbMath0099.08503OpenAlexW3195885320WikidataQ56227806 ScholiaQ56227806MaRDI QIDQ773798
Publication date: 1960
Published in: Acta Mathematica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02547186
Related Items
Solution of the Kirchhoff-Plateau problem, Structure of sets which are well approximated by zero sets of harmonic polynomials, Differentiability theorems for weak solutions of nonlinear elliptic differential equations, LOCAL SET APPROXIMATION: MATTILA–VUORINEN TYPE SETS, REIFENBERG TYPE SETS, AND TANGENT SETS, Gradient estimates in generalized Morrey spaces for parabolic operators, Unnamed Item, Measure theoretic geometry and elliptic variational problems, Morrey regularity for nonlinear elliptic equations with partial BMO nonlinearities under controlled growth, Weighted regularity estimates for a class of higher-order nonlinear parabolic and elliptic systems, An application of global gradient estimates in Lorentz-Morrey spaces: The existence of stationary solution to degenerate diffusive Hamilton-Jacobi equations, Morrey regularity of solutions to quasilinear elliptic equations over Reifenberg flat domains, Some New Constructions and Estimates in the Problem of Least Area, Metric Spaces of Shapes and Geometries Constructed from Set Parametrized Functions, Global gradient estimates for asymptotically regular problems of p(x)-Laplacian type, Weighted Orlicz estimates for general nonlinear parabolic equations over nonsmooth domains, Lorentz estimates for the gradient of weak solutions to elliptic obstacle problems with partially BMO coefficients, Unnamed Item, Unnamed Item, General methods of elliptic minimization, Rigidity and stability of submanifolds with entropy close to one, Weighted \(W^{1, p(\cdot)}\)-regularity for degenerate elliptic equations in Reifenberg domains, Global regularity estimates for Neumann problems of elliptic operators with coefficients having a BMO anti-symmetric part in NTA domains, Area-minimizing hypersurfaces in manifolds of Ricci curvature bounded below, Heat kernels and Hardy spaces on non-tangentially accessible domains with applications to global regularity of inhomogeneous Dirichlet problems, Gradient estimates of general nonlinear singular elliptic equations with measure data, W1,γ(·)-estimate to non-uniformly elliptic obstacle problems with borderline growth, Weighted variable Lorentz regularity for degenerate elliptic equations in Reifenberg domains, Parabolic Obstacle Problem with Measurable Coefficients in Morrey-Type Spaces, Good-\(\lambda \) and Muckenhoupt-Wheeden type bounds in quasilinear measure datum problems, with applications, Homogenization of the conormal derivative problem for elliptic systems in Reifenberg domains, Survey on gradient estimates for nonlinear elliptic equations in various function spaces, Early developments in geometric measure theory, Asymptotically regular operators in generalized Morrey spaces, Existence and regularity estimates for quasilinear equations with measure data: the case \(1 < p \leq (3n-2)/(2n-1)\), Minimization of Anisotropic Energies in Classes of Rectifiable Varifolds, Singularities of harmonic maps, Boundary Hölder regularity for elliptic equations, Discrete Reifenberg-type theorem, W1,p(⋅) regularity for quasilinear problems with irregular obstacles on Reifenberg domains, Nonlinear Muckenhoupt-Wheeden type bounds on Reifenberg flat domains, with applications to quasilinear Riccati type equations, The singular structure and regularity of stationary varifolds, Global weighted estimates for the gradient of solutions to nonlinear elliptic equations, Soap film spanning an elastic link, Symmetry and rigidity of minimal surfaces with Plateau-like singularities, A general regularity theory for stable codimension 1 integral varifolds, \(L^2\) curvature bounds on manifolds with bounded Ricci curvature, Lorentz–Morrey global bounds for singular quasilinear elliptic equations with measure data, Uniqueness property for \(2\)-dimensional minimal cones in \(\mathbb{R}^3\), Uniform local energy estimates and partial regularity for space partitions, Quasisymmetry and rectifiability of quasispheres, Up-to-boundary pointwise gradient estimates for very singular quasilinear elliptic equations with mixed data, Quasilinear divergence form elliptic equations in rough domains, Dirac and Plateau billiards in domains with corners, Gradient estimates in Orlicz spaces for nonlinear elliptic equations with BMO nonlinearity in nonsmooth domains, On the tangential properties of surfaces, Note on \(p\)-harmonic measure, Global estimates in Orlicz spaces for the gradient of solutions to parabolic systems, Surfaces Minimizing Area Plus Length of Singular Curves, Poisson kernel characterization of Reifenberg flat chord arc domains, Global gradient estimates in weighted Lebesgue spaces for parabolic operators, New gradient estimates for solutions to quasilinear divergence form elliptic equations with general Dirichlet boundary data, Soap films and soap bubbles: from Plateau to the olympic swimming pool in Beijing, Weighted \(L^p\)-estimates for elliptic equations with measurable coefficients in nonsmooth domains, Pointwise gradient estimates for a class of singular quasilinear equations with measure data, Global estimates for quasilinear parabolic equations on Reifenberg flat domains and its applications to Riccati type parabolic equations with distributional data, Weighted gradient estimates for elliptic problems with Neumann boundary conditions in Lipschitz and (semi-)convex domains, On Hölder regularity of the singular set of energy minimizing harmonic maps into closed manifolds, Parabolic equations with BMO nonlinearity in Reifenberg domains, Linearly approximatable functions, A mass reducing flow for real-valued flat chains with applications to transport networks, Explicit determination in \(\mathbb{R}^N\) of \((N-1)\)-dimensional area minimizing surfaces with arbitrary boundaries, Nonlinear Parabolic Equations with Variable Exponent Growth in Nonsmooth Domains, A Reifenberg type characterization for m-dimensional C^1-submanifolds of R^n, Weighted gradient estimates for higher order elliptic systems with non-smooth coefficients, Pointwise estimates for Stokes systems with BMO coefficients in Reifenberg domains, Plateau’s Problem, New volume comparison results and applications to degeneration of Riemannian metrics, Effective Reifenberg theorems in Hilbert and Banach spaces, Potential estimates of superquadratic elliptic systems with VMO coefficients in Reifenberg domains, Unnamed Item, Harnack's inequality for elliptic differential equations on minimal surfaces, Reifenberg's isoperimetric inequality revisited, Geometric Sobolev-like embedding using high-dimensional Menger-like curvature, Reifenberg parameterizations for sets with holes, Nonlinear Calderón-Zygmund theory involving dual data, Global weighted estimates for nonlinear elliptic obstacle problems over Reifenberg domains, Nonlinear elliptic equations with small BMO coefficients in nonsmooth domains in generalized Morrey spaces, Mean curvature flow, Rectifiability of the singular set of multiple-valued energy minimizing harmonic maps, Optimal regularity for nonlinear elliptic equations with righthand side measure in variable exponent spaces, Global weighted Lorentz estimates for parabolic equations with measure via strong fractional maximal functions, Unnamed Item, Unnamed Item, Regularity of free boundaries in anisotropic capillarity problems and the validity of Young's law, Generalized Morrey estimates for the gradient of divergence form parabolic operators with discontinuous coefficients, Reifenberg flatness of free boundaries in obstacle problems with VMO ingredients, Existence and regularity of solutions to elliptic calculus of variations problems among surfaces of varying topological type and singularity structure, Stability and continuity of functions of least gradient, Elliptic Obstacle Problems with Measurable Coefficients in Non-Smooth Domains, Potential Estimates and Quasilinear Parabolic Equations with Measure Data, Sliding stability and uniqueness for the set \((Y \times Y\), A comparison estimate for singular \(p\)-Laplace equations and its consequences, On the equality between the infima obtained by solving various Plateau's problems, Möbius-invariant self-avoidance energies for non-smooth sets of arbitrary dimension and co-dimension, 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, The regularity theory for the area functional (in geometric measure theory), Gradient estimates for a class of higher-order elliptic equations of \(p\)-growth over a nonsmooth domain, The Wiener criterion for nonlocal Dirichlet problems, Optimal Poisson kernel regularity for elliptic operators with Hölder continuous coefficients in vanishing chord-arc domains, Regularity in Orlicz spaces for quasi-linear elliptic equations of Schrödinger type, Small-constant uniform rectifiability, An end-point global gradient weighted estimate for quasilinear equations in non-smooth domains, Gradient estimates for elliptic equations with \(L^{p(\cdot )}\log L\) growth, Existence and regularity of solutions for nonlinear measure data problems with general growth, Boundary regularity and stability for spaces with Ricci bounded below, Global gradient estimates for spherical quasi-minimizers of integral functionals with \(p(x)\)-growth, Global \(W^{1,p(\cdot)}\) estimate for renormalized solutions of quasilinear equations with measure data on Reifenberg domains, The singular set of mean curvature flow with generic singularities, Regularity of almost-minimizers of Hölder-coefficient surface energies, A local description of 2-dimensional almost minimal sets bounded by a curve, Quantitative stability for the first Dirichlet eigenvalue in Reifenberg flat domains in \(\mathbb R^N\), Existence and soap film regularity of solutions to Plateau's problem, Regularity estimates for higher order elliptic systems on Reifenberg flat domains, Gradient estimates for parabolic equations in generalized weighted Morrey spaces, Covers, soap films and BV functions, Quasilinear equations with natural growth in the gradients in spaces of Sobolev multipliers, Existence of solutions to a general geometric elliptic variational problem, Harmonic measure on locally flat domains, Global weighted estimates for the nonlinear parabolic equations with non-standard growth, Global \(W^{1,p}\) estimates for elliptic systems in homogenization problems in Reifenberg domains, Topological minimal sets and existence results, Global gradient estimates for Dirichlet problems of elliptic operators with a BMO antisymmetric part, Soap films and covering spaces, \(C^{1+\alpha}\)-regularity for two-dimensional almost-minimal sets in \(\mathbb R^n\), Defects of liquid crystals with variable degree of orientation, Flatness of domains and doubling properties of measures supported on their boundary, with applications to harmonic measure, Interior and boundary \(W^{1,q}\)-estimates for quasi-linear elliptic equations of Schrödinger type, Regularity estimates for quasilinear elliptic equations with variable growth involving measure data, Parabolic equations in time dependent Reifenberg domains, Global gradient estimates for general nonlinear parabolic equations in nonsmooth domains, Hard Sard: quantitative implicit function and extension theorems for Lipschitz maps, Global regularity for divergence form elliptic equations on quasiconvex domains, Gradient estimates for higher order elliptic equations on nonsmooth domains, New monotonicity formulas for Ricci curvature and applications. I, Weighted Lorentz estimates for parabolic equations with non-standard growth on rough domains, Integral Menger curvature for surfaces, The Steiner problem for infinitely many points, \(W^{1,p}\) regularity of weak solutions to Maxwell's equations, A direct approach to Plateau's problem in any codimension, The Calderón-Zygmund property for quasilinear divergence form equations over Reifenberg flat domains, Weighted and regularity estimates for nonlinear equations on Reifenberg flat domains, Quasilinear Riccati type equations with distributional data in Morrey space framework, Rectifiability of line defects in liquid crystals with variable degree of orientation, Triple covers and a non-simply connected surface spanning an elongated tetrahedron and beating the cone, Regularity theory for almost minimal currents, Elliptic equations with measurable coefficients in Reifenberg domains, Gradient estimates for elliptic systems in non-smooth domains, Soap film solutions to Plateau's problem, Global Calderón-Zygmund theory for nonlinear elliptic obstacle problems with asymptotically regular nonlinearities, Weak limits of quasiminimizing sequences, A direct approach to the anisotropic Plateau problem, Soap-film-like minimal surfaces spanning knots, Solutions to the Reifenberg plateau problem with cohomological spanning conditions, Existence results for minimizers of parametric elliptic functionals, Rectifiable-Reifenberg and the regularity of stationary and minimizing harmonic maps, Canonical decompositions of piecewise affine mappings, polyhedra-traces, and geometrical variational problems, Elliptic equations with BMO nonlinearity in Reifenberg domains, Lorentz gradient estimates for a class of elliptic \(p\)-Laplacian equations with a Schrödinger term, Global gradient estimates for the borderline case of double phase problems with BMO coefficients in nonsmooth domains, Fourth-order parabolic equations with weak BMO coefficients in Reifenberg domains, Global Lorentz estimates for nonlinear parabolic equations on nonsmooth domains, Gradient estimates in Orlicz space for nonlinear elliptic equations, A regularity theorem for curvature flows, A direct approach to Plateau's problem, A stability result for nonlinear Neumann problems in Reifenberg flat domains in \(\mathbb R^N\), \(L^p\) estimates for parabolic equations in Reifenberg domains, Nonlinear gradient estimates for parabolic obstacle problems in non-smooth domains, Quasiconformal planes with bi-Lipschitz pieces and extensions of almost affine maps, Parabolic equations in Reifenberg domains, Global estimates for quasilinear elliptic equations on Reifenberg flat domains, Weighted variable exponent Sobolev estimates for elliptic equations with non-standard growth and measure data, Gradient estimates for elliptic systems with measurable coefficients in nonsmooth domains, Pointwise gradient bounds for a class of very singular quasilinear elliptic equations, On \(W^{1,q(\cdot)}\)-estimates for elliptic equations of \(p(x)\)-Laplacian type, Convex functionals and the stratification of the singular set of their stationary points, Calderón-Zygmund estimate for homogenization of parabolic systems, Nonlinear elliptic equations with BMO coefficients in Reifenberg domains, Comparing homologies: Čech's theory, singular chains, integral flat chains and integral currents, Mean curvature flow of arbitrary co-dimensional Reifenberg sets, Stratification for the singular set of approximate harmonic maps, Weighted global regularity estimates for elliptic problems with Robin boundary conditions in Lipschitz domains, Optimal regularity for a Dirichlet-conormal problem in Reifenberg flat domain, Regularity of minimal and CMC stable hypersurfaces: a brief overview, Geometric conditions and existence of bi-Lipschitz parameterizations, The singular set of an energy minimizing map from \(B^ 4\) to \(S^ 2\), Hessian estimates in Orlicz spaces for fourth-order parabolic systems in non-smooth domains, Hölder regularity of two-dimensional almost-minimal sets in \(\mathbb R^n\), Existence and \(W^{1,p}\) estimates of certain Maxwell type equations in Reifenberg domains, A regularity theorem for geometric equations, The restricted content and the \(d\)-dimensional Analyst's travelling salesman theorem for general sets, On the oriented Plateau problem, A remark on two notions of flatness for sets in the Euclidean space, On the two-phase membrane problem with coefficients below the Lipschitz threshold, Solutions of the (free boundary) Reifenberg Plateau problem, Regularity of the singular sets of two-dimensional area-minimizing flat chains modulo 3 in R\(^3\), Gradient estimates of parabolic Cauchy-Dirichlet problems on Morrey-Banach spaces, Gradient estimates via Riesz potentials and fractional maximal operators for quasilinear elliptic equations with applications, Characterising rectifiable metric spaces using tangent spaces, Lagrange multipliers and geometric measure theory, Nearly flat almost monotone measures are big pieces of Lipschitz graphs, Lorentz-Morrey regularity for nonlinear elliptic problems with irregular obstacles over Reifenberg flat domains
Cites Work
- Minimal surfaces of higher topological structure
- Parametrizations of Saddle Surfaces, with Application to the Problem of Plateau
- A general form of the covering principle and relative differentiation of additive functions
- Parametric Surfaces (V). Area II
- On the fundamental geometrical properties of linearly measurable plane sets of points. II
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item