Mean curvature flow singularities for mean convex surfaces
From MaRDI portal
Publication:1283877
DOI10.1007/s005260050113zbMath0992.53052OpenAlexW2095345234MaRDI QIDQ1283877
Gerhard Huisken, Carlo Sinestrari
Publication date: 31 May 1999
Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: http://hdl.handle.net/11858/00-001M-0000-0013-5853-1
Nonlinear parabolic equations (35K55) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12)
Related Items
Convexity of 2-convex translating and expanding solitons to the mean curvature flow in \(\mathbb{R}^{n+1}\), Collapsing and noncollapsing in convex ancient mean curvature flow, Local convexity estimates for mean curvature flow, Local entropy and generic multiplicity one singularities of mean curvature flow of surfaces, Evolution of form and shape, Snapshots of non-local constrained mean curvature-type flows, Numerical Surgery for Mean Curvature Flow of Surfaces, Mean curvature flow with surgery of mean convex surfaces in \(\mathbb R^3\), Translating solitons of translation and homothetical types, On Ilmanen's multiplicity-one conjecture for mean curvature flow with type-\(I\) mean curvature, The nature of singularities in mean curvature flow of mean-convex sets, \(K\)-mean convex and \(K\)-outward minimizing sets, Convexity estimates for mean curvature flow with free boundary, Dirichlet problem for anisotropic prescribed mean curvature equation on unbounded domains, Spacelike translating solitons in Lorentzian product spaces: Nonexistence, Calabi–Bernstein type results and examples, Compact translating solitons with non-empty planar boundary, The singular set of mean curvature flow with generic singularities, Mean Curvature Flow in Higher Codimension: Introduction and Survey, Blow-up of the mean curvature at the first singular time of the mean curvature flow, The Dirichlet problem on a strip for the \(\alpha\)-translating soliton equation, Quantitative stratification and the regularity of mean curvature flow, Volume growth and Bernstein theorems for translating solitons, Bifurcation of perturbations of non-generic closed self-shrinkers, The area preserving curve shortening flow with Neumann free boundary conditions, On the complete 2-dimensional \(\lambda\)-translators with a second fundamental form of constant length, Bi-Halfspace and Convex Hull Theorems for Translating Solitons, Properness of translating solitons for the mean curvature flow, Mean curvature flow with a constant forcing, Convexity estimates for hypersurfaces moving by concave curvature functions, Complete embedded self-translating surfaces under mean curvature flow, Rigidity of symplectic translating solitons, Rotationally symmetric spacelike translating solitons for the mean curvature flow in Minkowski space, A general pinching principle for mean curvature flow and applications, A pinching estimate for convex hypersurfaces evolving under a non-homogeneous variant of mean curvature flow, Finite topology self-translating surfaces for the mean curvature flow in \(\mathbb{R}^3\), Stability of translating solutions to mean curvature flow, A sharp bound for the inscribed radius under mean curvature flow, Unnamed Item, Uniqueness of convex ancient solutions to mean curvature flow in \({\mathbb {R}}^3\), The mean curvature at the first singular time of the mean curvature flow, Translating solitons for the inverse mean curvature flow, Stability of the surface area preserving mean curvature flow in Euclidean space, Helicoidal surfaces rotating/translating under the mean curvature flow, Generic mean curvature flow. I: Generic singularities, Hamiltonian L-stability of Lagrangian translating solitons, Complete 3-dimensional \(\lambda \)-translators in the Minkowski space \(\mathbb{R}^4_1 \), Sharp one-sided curvature estimates for fully nonlinear curvature flows and applications to ancient solutions, On the extension of the mean curvature flow, Existence of translating solutions to the flow by powers of mean curvature on unbounded domains, Mean Curvature Flow of Mean Convex Hypersurfaces, Non-collapsing in fully non-linear curvature flows, Translating solitons of mean curvature flow of noncompact submanifolds, Heisenberg isoperimetric problem. The axial case, Translating solitons foliated by spheres, Rigidity results and topology at infinity of translating solitons of the mean curvature flow, Partial regularity at the first singular time for hypersurfaces evolving by mean curvature, Convex solutions to the mean curvature flow, The classification of constant weighted curvature curves in the plane with a log-linear density, Entire spacelike translating solitons in Minkowski space, Translating solitons to symplectic mean curvature flows, Mean curvature decay in symplectic and Lagrangian translating solitons, Fully nonlinear curvature flow of axially symmetric hypersurfaces with boundary conditions, A uniqueness theorem of complete Lagrangian translator in \(\mathbb C^2\), Pinched ancient solutions to the high codimension mean curvature flow, Translating solitons in Riemannian products, Analytical Properties for Degenerate Equations, Ruled translating solitons in Minkowski 3-space, Mean curvature flow solitons in the presence of conformal vector fields, Invariant surfaces in Euclidean space with a log-linear density, Some geometric properties of translating solitons in Euclidean space, Ancient solutions in Lagrangian mean curvature flow, Compact \(\lambda \)-translating solitons with boundary, Nonlinear degenerate curvature flows for weakly convex hypersurfaces, The second type singularities of symplectic and Lagrangian mean curvature flows, A family of parameter-dependent diffeomorphisms acting on function spaces over a Riemannian manifold and applications to geometric flows, Minimum principles and a priori estimates for some translating soliton type problems, Singularity structure in mean curvature flow of mean-convex sets, A Bernstein type theorem of ancient solutions to the mean curvature flow, Convexity estimates for a nonhomogeneous mean curvature flow, Existence and asymptotic behavior of helicoidal translating solitons of the mean curvature flow, Type-II singularities of two-convex immersed mean curvature flow, Uniqueness of the bowl soliton, Mean curvature flow with surgeries of two-convex hypersurfaces, Curve flows with a global forcing term, Classification theorems of complete space-like Lagrangian \(\xi\)-surfaces in the pseudo-Euclidean space \(\mathbb{R}^4_2\), TRANSLATING SOLITONS TO SYMPLECTIC AND LAGRANGIAN MEAN CURVATURE FLOWS, On mean curvature flow with forcing, A Class of Parabolic Equations Driven by the Mean Curvature Flow, Translating solutions to mean curvature flow, The translating soliton equation, Flowing the leaves of a foliation with normal speed given by the logarithm of general curvature functions, Surfaces with a canonical principal direction and prescribed mean curvature, Neck pinching dynamics under mean curvature flow, Differentiability of the Arrival Time, Conformal solitons to the mean curvature flow and minimal submanifolds, On the type IIb solutions to mean curvature flow, Singularities of symplectic and Lagrangian mean curvature flows, On asymptotic behavior for singularities of the powers of mean curvature flow, Mean curvature flow, The extension problem of the mean curvature flow (I), Convexity estimates for mean curvature flow and singularities of mean convex surfaces, Half-space type theorem for translating solitons of the mean curvature flow in Euclidean space, A Bernstein type result of translating solitons, Translating graphs by mean curvature flow, Rigidity results on Lagrangian and symplectic translating solitons, Ancient mean curvature flows out of polytopes, Uniqueness of blowups and Łojasiewicz inequalities, Subsequent singularities of mean convex mean curvature flows in smooth manifolds