The first Steklov eigenvalue, conformal geometry, and minimal surfaces

From MaRDI portal
Publication:631794

DOI10.1016/j.aim.2010.11.007zbMath1215.53052arXiv0912.5392OpenAlexW2041867826MaRDI QIDQ631794

Ailana M. Fraser, Richard M. Schoen

Publication date: 14 March 2011

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.5392




Related Items (only showing first 100 items - show all)

Rigidity of minimal hypersurfaces with free boundary in a ballNumerical calculation of extremal Steklov eigenvalues in 3D and 4DUpper bounds for the Steklov eigenvalues on treesSome sharp Hodge Laplacian and Steklov eigenvalue estimates for differential formsTrace and inverse trace of Steklov eigenvaluesNyström methods and extrapolation for solving Steklov eigensolutions and its application in elasticityLarge spectral gaps for Steklov eigenvalues under volume constraints and under localized conformal deformationsAlexandrov-Fenchel inequalities for convex hypersurfaces with free boundary in a ballSpectral invariants of the perturbed polyharmonic Steklov problemA compactness theorem of the space of free boundary \(f\)-minimal surfaces in three-dimensional smooth metric measure space with boundaryShape optimization for the Steklov problem in higher dimensionsRigidity of free boundary surfaces in compact 3-manifolds with strictly convex boundaryHarmonic maps with prescribed degrees on the boundary of an annulus and bifurcation of catenoidsEstimates of the first Steklov eigenvalue of properly embedded minimal hypersurfaces with free boundaryRecent rigidity results for graphs with prescribed mean curvatureCompactness and generic finiteness for free boundary minimal hypersurfaces. IA new eigenvalue problem for free boundary minimal submanifolds in the unit ballExistence and classification of \(\mathbb{S}^1\)-invariant free boundary minimal annuli and Möbius bands in \(\mathbb{B}^n\)Stability for a second type partitioning problemArea estimates and rigidity of capillary \(H\)-surfaces in three-manifolds with boundaryMin-max minimal disks with free boundary in Riemannian manifoldsMean curvature flow with free boundary in embedded cylinders or cones and uniqueness results for minimal hypersurfacesA characterization of the disk by eigenfunction of the Steklov eigenvalueFree boundary minimal surfaces in the unit 3-ballOn stable constant mean curvature surfaces with free boundaryNonnegatively curved hypersurfaces with free boundary on a sphereGeometric inequalities for free boundary hypersurfaces in a ballEvolution of the Steklov eigenvalue under geodesic curvature flowSteklov eigenvalues of submanifolds with prescribed boundary in Euclidean spaceOn the index of the critical Möbius band in \(\mathbb{B}^4\)On the Steklov spectrum of covering spaces and total spacesA sharp bound for the area of minimal surfaces in the unit ballFree boundary constant p-mean curvature surfaces intersecting the Pansu sphereFree boundary minimal surfaces in the unit ball with low cohomogeneityWidths of balls and free boundary minimal submanifoldsInequivalent complexity criteria for free boundary minimal surfacesOn the Morse index with constraints for capillary surfacesUniqueness of the catenoid and the Delaunay surface via a one-parameter family of touching spheresCompactness analysis for free boundary minimal hypersurfacesEstimates for higher Steklov eigenvaluesSome results on higher eigenvalue optimizationEigenvalues of the Wentzell-Laplace operator and of the fourth order Steklov problemsIndex bounds for free boundary minimal surfaces of convex bodiesThe relative isoperimetric inequality for minimal submanifolds with free boundary in the Euclidean spaceIndex estimates for free boundary minimal hypersurfacesA gap theorem for free boundary minimal surfaces in geodesic balls of hyperbolic space and hemisphereConformal upper bounds for the eigenvalues of the Laplacian and Steklov problemVariational aspects of Laplace eigenvalues on Riemannian surfacesRigidity of a trace estimate for Steklov eigenvaluesHigher genus capillary surfaces in the unit ball of \(\mathbb R^3\)The Steklov Problem on Differential FormsMinimal hypersurfaces in the ball with free boundaryMultiplicity bounds for Steklov eigenvalues on Riemannian surfacesIndex of the critical catenoidContinuity of eigenvalues and shape optimisation for Laplace and Steklov problemsExtremal problems for Steklov eigenvalues on annuliUniqueness results for free boundary minimal hypersurfaces in conformally Euclidean balls and annular domainsOn the Morse index of higher-dimensional free boundary minimal catenoidsUpper bounds for the first non-zero Steklov eigenvalue via anisotropic mean curvaturesDeformations of free boundary CMC hypersurfacesEstimates for eigenvalues of the Wentzell-Laplace operatorA Reilly inequality for the first non-zero eigenvalue of a class of operators on Riemannian manifoldStability of capillary hypersurfaces with planar boundariesGeneralizations of the Choe-Hoppe helicoid and Clifford cones in Euclidean spaceCatenoidal layers for the Allen-Cahn equation in bounded domainsFree boundary minimal surfaces and overdetermined boundary value problemsBounds between Laplace and Steklov eigenvalues on nonnegatively curved manifoldsCompactness and bubble analysis for 1/2-harmonic mapsIsoperimetric control of the Steklov spectrumExistence and geometric structure of metrics on surfaces which extremize eigenvaluesA partially overdetermined problem in a half ballA Reilly inequality for the first Steklov eigenvalueOn the relative heat invariants of the Dirichlet-to-Neumann operators associated with Schrödinger operatorsTrace and inverse trace of Steklov eigenvalues. II.A remark on a curvature gap for minimal surfaces in the ballWeinstock inequality in higher dimensionsStability of capillary hypersurfaces in a Euclidean ballA splitting theorem for capillary graphs under Ricci lower boundsOn asymptotic properties of biharmonic Steklov eigenvaluesFree boundary minimal surfaces in the unit three-ball via desingularization of the critical catenoid and the equatorial discA two-piece property for free boundary minimal surfaces in the ballNodal sets of Steklov eigenfunctionsLarge Steklov eigenvalues via homogenisation on manifoldsIndex estimates for free boundary constant mean curvature surfacesThe Morse index of the critical catenoidUniqueness of stable capillary hypersurfaces in a ballMaximal convex combinations of sequential Steklov eigenvaluesEvolution of the Steklov eigenvalue along the conformal mean curvature flowOn second-order and fourth-order elliptic systems consisting of bulk and surface PDEs: well-posedness, regularity theory and eigenvalue problemsArea bounds for free boundary minimal surfaces in a geodesic ball in the sphereComputation of free boundary minimal surfaces via extremal Steklov eigenvalue problemsOn the elliptic sinh–Gordon equation with integrable boundary conditions *Stable capillary hypersurfaces supported on a horosphere in the hyperbolic spaceHeat invariants of the Steklov problemAsymptotic expansion of the trace of the heat kernel associated to the Dirichlet-to-Neumann operatorA free boundary isometric embedding problem in the unit ballFree boundary constant mean curvature surfaces in a strictly convex three-manifoldOn the spectra of three Steklov eigenvalue problems on warped product manifoldsLaplace and Steklov extremal metrics via \(n\)-harmonic mapsSharp eigenvalue bounds and minimal surfaces in the ball



Cites Work


This page was built for publication: The first Steklov eigenvalue, conformal geometry, and minimal surfaces