Deforming a hypersurface by its Gauss-Kronecker curvature
From MaRDI portal
Publication:3753038
DOI10.1002/cpa.3160380615zbMath0612.53005OpenAlexW2016684934MaRDI QIDQ3753038
Publication date: 1985
Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/cpa.3160380615
Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Initial value problems for linear higher-order PDEs (35G10) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Higher-order parabolic equations (35K25)
Related Items (only showing first 100 items - show all)
Contraction of convex hypersurfaces in Euclidean space ⋮ On a non-homogeneous version of a problem of Firey ⋮ Convex mean curvature flow with a forcing term in direction of the position vector ⋮ A unified flow approach to smooth, even \(L_p\)-Minkowski problems ⋮ On a logarithmic type nonlocal plane curve flow ⋮ Entire solutions of Cauchy problem for parabolic Monge-Ampère equations ⋮ Deforming convex hypersurfaces by the square root of the scalar curvature ⋮ The \(L_{p}\)-Minkowski problem for \(-n < p < 1\) ⋮ Harnack inequalities for evolving hypersurfaces ⋮ Evolving plane curves by curvature in relative geometries. II ⋮ Flow by powers of the Gauss curvature ⋮ The first initial-boundary value problem for Hessian equations of parabolic type on Riemannian manifolds ⋮ Deforming a hypersurface by Gauss curvature and support function ⋮ A Calabi theorem for solutions to the parabolic Monge-Ampère equation with periodic data ⋮ Evolution of convex entire graphs by curvature flows ⋮ Uniqueness of convex ancient solutions to hypersurface flows ⋮ An extension of Jörgens-Calabi-Pogorelov theorem to parabolic Monge-Ampère equation ⋮ Contracting convex hypersurfaces by curvature ⋮ Curvature contraction of convex hypersurfaces by nonsmooth speeds ⋮ Curvature flow in hyperbolic spaces ⋮ Volume-preserving nonhomogeneous mean curvature flow of convex hypersurfaces ⋮ Convex sets evolving by volume-preserving fractional mean curvature flows ⋮ Li-Yau inequalities in geometric analysis ⋮ Contracting axially symmetric hypersurfaces by powers of the \(\sigma_k\)-curvature ⋮ Regularity estimates for solutions to the mean curvature flow with a Neumann boundary condition ⋮ Isometric deformations of the \({\mathcal K}^{\frac{1}{4}}\)-flow translators in \(\mathbb{R}^3\) with helicoidal symmetry ⋮ Volume preserving flow by powers of symmetric polynomials in the principal curvatures ⋮ Volume preserving flows for convex curves and surfaces in the hyperbolic space ⋮ Convergence of solutions to the mean curvature flow with a Neumann boundary condition ⋮ Moving surfaces by non-concave curvature functions ⋮ A fully nonlinear flow for two-convex hypersurfaces in Riemannian manifolds ⋮ Regularity results for fully nonlinear parabolic integro-differential operators ⋮ A flow approach to the fractional Minkowski problem ⋮ On Jörgens, Calabi, and Pogorelov type theorem and isolated singularities of parabolic Monge-Ampère equations ⋮ Entropy and a convergence theorem for Gauss curvature flow in high dimension ⋮ Ancient solutions of geometric flows with curvature pinching ⋮ Smooth solutions to the \(L_p\) dual Minkowski problem ⋮ Translators of flows by powers of the Gauss curvature ⋮ Existence for translating solutions of Gauss curvature flow on exterior domains ⋮ Non-homothetic convex ancient solutions for flows by high powers of curvature ⋮ The centro-affine invariant geometric heat flow ⋮ Pinched hypersurfaces are compact ⋮ A maximum problem of S.-T. Yau for variational \(p\)-capacity ⋮ Weak regularity of Gauss mass transport ⋮ Multi-valued solutions to a class of parabolic Monge-Ampère equations ⋮ The blow up analysis of the general curve shortening flow ⋮ Uniqueness of closed self-similar solutions to \(\sigma_k^\alpha\)-curvature flow ⋮ Generalized motion of level sets by functions of their curvatures on Riemannian manifolds ⋮ On an area-preserving inverse curvature flow of convex closed plane curves ⋮ Volume preserving flow by powers of the \(k\)-th mean curvature ⋮ Anisotropic flows for convex plane curves ⋮ Translating solutions to the Gauss curvature flow with flat sides ⋮ Convex bodies with pinched Mahler volume under the centro-affine normal flows ⋮ Boundary regularity on the parabolic Monge-Ampère equation ⋮ Invariant hypersurface flows in centro-affine geometry ⋮ Forced convex mean curvature flow in Euclidean spaces ⋮ More mixed volume preserving curvature flows ⋮ Flow of pinched convex hypersurfaces by powers of curvature functions in hyperbolic space ⋮ On Yau's problem of evolving one curve to another: convex case ⋮ A Liouville theorem of parabolic Monge-Ampère equations in half-space ⋮ Area-preserving evolution of nonsimple symmetric plane curves ⋮ Characterization of Besov spaces associated with parabolic sections ⋮ Symmetry of solutions to parabolic Monge-Ampère equations ⋮ The logarithmic Minkowski problem for polytopes ⋮ Contraction of surfaces in hyperbolic space and in sphere ⋮ Nonlinear degenerate curvature flows for weakly convex hypersurfaces ⋮ The evolution of complete non-compact graphs by powers of Gauss curvature ⋮ Existence of multi-valued solutions with asymptotic behavior of parabolic Monge-Ampère equation ⋮ Deforming a convex hypersurface with low entropy by its Gauss curvature ⋮ Volume-preserving flow by powers of the \(m\)th mean curvature ⋮ Triangular surface mesh fairing via Gaussian curvature flow ⋮ ON A CURVE EXPANDING FLOW WITH A NON-LOCAL TERM ⋮ The planar Busemann-Petty centroid inequality and its stability ⋮ The obstacle problem for the Monge-Ampère equation with the lower obstacle ⋮ Quermassintegral preserving curvature flow in hyperbolic space ⋮ Mass transport generated by a flow of Gauss maps ⋮ Volume preserving flow and Alexandrov-Fenchel type inequalities in hyperbolic space ⋮ On a non-local perimeter-preserving curve evolution problem for convex plane curves ⋮ A general framework for surface modeling using geometric partial differential equations ⋮ Contraction of convex hypersurfaces by nonhomogeneous functions of curvature ⋮ Gauss curvature flow with an obstacle ⋮ Convex hypersurfaces evolving by volume preserving curvature flows ⋮ Contracting convex hypersurfaces in space form by non-homogeneous curvature function ⋮ Smoothness in the \(L_p\) Minkowski problem for \(p<1\) ⋮ Asymptotic convergence for a class of fully nonlinear curvature flows ⋮ Curvature flow with a general forcing term in Euclidean spaces ⋮ Flowing the leaves of a foliation with normal speed given by the logarithm of general curvature functions ⋮ Convex hypersurfaces with pinched principal curvatures and flow of convex hypersurfaces by high powers of curvature ⋮ Evolving a convex closed curve to another one via a length-preserving linear flow ⋮ A class of Gauss curvature flows and its applications to an even dual Orlicz-Minkowski type problem ⋮ Contracting convex immersed closed plane curves with slow speed of curvature ⋮ On asymptotic behavior for singularities of the powers of mean curvature flow ⋮ Mixed volume preserving curvature flows ⋮ The Orlicz version of the \(L_p\) Minkowski problem for \(- n < p < 0\) ⋮ Evolution of convex hypersurfaces by powers of the mean curvature ⋮ A logarithmic Gauss curvature flow and the Minkowski problem. ⋮ Convergence of a three-dimensional crystalline motion to Gauss curvature flow ⋮ The \(L_p\) Minkowski problem for polytopes for \(0 < p < 1\) ⋮ Nonuniqueness of solutions to the \(L_p\)-Minkowski problem ⋮ The planar \(L_{p}\)-Minkowski problem for \(0<p<1\)
Cites Work
This page was built for publication: Deforming a hypersurface by its Gauss-Kronecker curvature
