Interior estimates for hypersurfaces moving by mean curvature
From MaRDI portal
Publication:919625
DOI10.1007/BF01232278zbMath0707.53008WikidataQ126049599 ScholiaQ126049599MaRDI QIDQ919625
Publication date: 1991
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/143923
maximum principlemean curvature flowcurvaturegradienthypersurfacesheat equationstime dependent metric
Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Heat and other parabolic equation methods for PDEs on manifolds (58J35)
Related Items
On Ilmanen's multiplicity-one conjecture for mean curvature flow with type-\(I\) mean curvature, Mean curvature flow with a forcing term in Minkowski space, Contraction of convex hypersurfaces in Euclidean space, Weak solutions for a stochastic mean curvature flow of two-dimensional graphs, Volume comparison of conformally compact manifolds with scalar curvature \(R\geq -n(n-1)\), Evolution of noncompact hypersurfaces by inverse mean curvature, Construction of maximal hypersurfaces with boundary conditions, Lagrangian mean curvature flow with boundary, Self-shrinkers with bounded \(|HA|\), Area-preserving mean curvature flow of rotationally symmetric hypersurfaces with free boundaries, Mean Curvature Flow in Higher Codimension: Introduction and Survey, On regularity for mean curvature flow of hypersurfaces, A new length estimate for curve shortening flow and low regularity initial data, Non-parametric radially symmetric mean curvature flow with a free boundary, Evolution of convex entire graphs by curvature flows, Renormalized volume and the evolution of apes, An interior gradient estimate for the mean curvature equation of Killing graphs and applications, Uniqueness of convex ancient solutions to hypersurface flows, Mean curvature flow through singularities for surfaces of rotation, Rotational symmetry of solutions of mean curvature flow coming out of a double cone, An example of a mean-convex mean curvature flow developing infinitely many singular epochs, Curvature flow in hyperbolic spaces, Convergence of Ricci flow on a class of warped product metrics, Spacelike mean curvature flow, Extension of two-dimensional mean curvature flow with free boundary, Volume-preserving mean curvature flow for tubes in rank one symmetric spaces of non-compact type, Existence of martingale solutions and large-time behavior for a stochastic mean curvature flow of graphs, Lagrangian mean curvature flow for entire Lipschitz graphs. II, Volume preserving mean curvature flow for star-shaped sets, Rigidity and stability of submanifolds with entropy close to one, Expanding solitons with non-negative curvature operator coming out of cones, A fully nonlinear flow for two-convex hypersurfaces in Riemannian manifolds, Gradient estimates for mean curvature flow with Neumann boundary conditions, Mean curvature flow with free boundary in embedded cylinders or cones and uniqueness results for minimal hypersurfaces, Closed hypersurfaces of low entropy in \({\mathbb{R}^4}\) are isotopically trivial, Stability of translating solutions to mean curvature flow, A note on Grayson's theorem, On scalar curvature lower bounds and scalar curvature measure, The level-set flow of the topologist's sine curve is smooth, Rotational symmetry of solutions of mean curvature flow coming out of a double cone. II., The mean curvature at the first singular time of the mean curvature flow, The Yamabe flow on asymptotically Euclidean manifolds with nonpositive Yamabe constant, The positive mass theorem for non-spin manifolds with distributional curvature, Uniqueness of entire graphs evolving by mean curvature flow, Inverse mean curvature flow of rotationally symmetric hypersurfaces, Pinched hypersurfaces are compact, On the compactness of hypersurfaces with finite total curvature via mean curvature flow, Partial regularity at the first singular time for hypersurfaces evolving by mean curvature, Large time behavior of disturbed planar fronts in the Allen-Cahn equation, Evolution of area-decreasing maps between two-dimensional Euclidean spaces, Dynamics of closed singularities, Asymptotic behavior and stability of mean curvature flow with a conical end, Yamabe flow and Myers type theorem on complete manifolds, Evolution of convex lens-shaped networks under the curve shortening flow, Uniqueness of convex ancient solutions to mean curvature flow in higher dimensions, Bounded diameter under mean curvature flow, Mean curvature flow of contractions between Euclidean spaces, A curve shortening equation with time-dependent mobility related to grain boundary motions, On short time existence of Lagrangian mean curvature flow, No mass drop for mean curvature flow of mean convex hypersurfaces, Mean curvature flow with convex Gauss image, Mean curvature flow with bounded Gauss image, The evolution of complete non-compact graphs by powers of Gauss curvature, The heat flow in nonlinear Hodge theory, Maximum principle and convergence of fundamental solutions for the Ricci flow, A note on the backwards uniqueness of the mean curvature flow, Total mass under connection Ricci flow, A Liouville theorem for superlinear heat equations on Riemannian manifolds, The space of asymptotically conical self-expanders of mean curvature flow, Ancient and eternal solutions to mean curvature flow from minimal surfaces, Type-II singularities of two-convex immersed mean curvature flow, Motion by curvature of networks with two triple junctions, Mean curvature flow of arbitrary co-dimensional Reifenberg sets, Modica Type Gradient Estimates for Reaction-Diffusion Equations, Regularity of inverse mean curvature flow in asymptotically hyperbolic manifolds with dimension 3, Mean curvature flow in asymptotically flat product spacetimes, Lipschitz bounds for solutions of quasilinear parabolic equations in one space variable, General initial data for a class of parabolic equations including the curve shortening problem, Curvature decay estimates of graphical mean curvature flow in higher codimensions, Uniqueness of asymptotically conical tangent flows, Collapsing ancient solutions of mean curvature flow, Mean curvature flow of graphs in warped products, On the type IIb solutions to mean curvature flow, Short-time existence for harmonic map heat flow with time-dependent metrics, Ricci flow of non-collapsed three manifolds whose Ricci curvature is bounded from below, A mountain-pass theorem for asymptotically conical self-expanders, Backwards uniqueness of the mean curvature flow, The extension problem of the mean curvature flow (I), Approximation of mean curvature flow with generic singularities by smooth flows with surgery, A probabilistic method for gradient estimates of some geometric flows, Ancient mean curvature flows out of polytopes, Uniqueness for parabolic equations without growth condition and applications to the mean curvature flow in \(\mathbb R^2\), Interior estimates for translating solitons of the \(Q_k\)-flows in \(\mathbb{R}^{n+1}\), Singularity models of pinched solutions of mean curvature flow in higher codimension, Inverse mean curvature evolution of entire graphs, The \(Q_k\) flow on complete non-compact graphs, Uniqueness of blowups and Łojasiewicz inequalities, Eventual regularity for the parabolic minimal surface equation, Rigidity of generic singularities of mean curvature flow, Relative expander entropy in the presence of a two-sided obstacle and applications, ALMOST RIGIDITY OF CONVEX HYPERSURFACES VIA THE EXTINCTION TIME OF MEAN CURVATURE FLOW, Yamabe flow and ADM mass on asymptotically flat manifolds, Mean curvature flow of entire graphs evolving away from the heat flow, Smooth Compactness for Spaces of Asymptotically Conical Self-Expanders of Mean Curvature Flow, Uniqueness of self-similar shrinkers with asymptotically conical ends, The limit of the inverse mean curvature flow on a torus, On the precise asymptotics of Type-IIb solutions to mean curvature flow, Local derivative estimates for the heat equation coupled to the Ricci flow, Existence of mean curvature flow singularities with bounded mean curvature, Rigidity results for mean curvature flow graphical translators moving in non-graphical direction, The Yamabe flow on asymptotically flat manifolds, A de Sitter no-hair theorem for 3+1d cosmologies with isometry group forming 2-dimensional orbits, CURVE SHORTENING FLOWS ON ROTATIONAL SURFACES GENERATED BY MONOTONE CONVEX FUNCTIONS, Curve shortening flows in warped product manifolds, Entire convex curvature flow in Minkowski space, Collapsing and noncollapsing in convex ancient mean curvature flow, Multiplicity results for discrete partial mean curvature problems, Curvature evolution of plane curves with prescribed opening angle, Convexity estimates for high codimension mean curvature flow, Evolution of graphs in hyperbolic space by their Gauss curvature, On the \(H^1 (ds^{\gamma})\)-gradient flow for the length functional, Stability of self-similar solutions to geometric flows, Convergence of diffusion generated motion to motion by mean curvature, Mean curvature flow with free boundary outside a hypersphere, Pulsating wave for mean curvature flow in inhomogeneous medium, Gradient Estimates for Spacelike Mean Curvature Flow with Boundary Conditions, Analysis of Velázquez’s solution to the mean curvature flow with a type II singularity, A C0-estimate for the parabolic Monge–Ampère equation on complete non-compact Kähler manifolds, Minimal surfaces in minimally convex domains, Time-periodic solutions of quasilinear parabolic differential equations. I: Dirichlet boundary conditions, Curvature evolution of nonconvex lens-shaped domains, A rigidity theorem on the second fundamental form for self-shrinkers, Uniqueness without Growth Condition for the Mean Curvature Equation with Radial Initial Data, Entire spacelike hypersurfaces of constant Gauß curvature in Minkowski space, Mean curvature flow with surgery of mean convex surfaces in \(\mathbb R^3\), Mean curvature flow of asymptotically conical Lagrangian submanifolds, Ancient solutions to the Curve Shortening Flow spanning the halfplane, On mean curvature flow with forcing, Mean curvature flow, An example of three dimensional fattening for linked space curves evolving by curvature
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the heat equation for harmonic maps from non-compact manifolds
- Flow by mean curvature of convex surfaces into spheres
- Asymptotic behavior for singularities of the mean curvature flow
- A Bernstein result for minimal graphs of controlled growth
- Mean curvature evolution of entire graphs
- Contracting convex hypersurfaces in Riemannian manifolds by their mean curvature
- The heat equation shrinks embedded plane curves to round points
- Deforming the metric on complete Riemannian manifolds
- Evolutionary surfaces of prescribed mean curvature
- Non-parametric mean curvature evolution with boundary conditions
- Three-manifolds with positive Ricci curvature
- The Motion of a Surface by Its Mean Curvature. (MN-20)