The Christoffel-Minkowski problem. I: Convexity of solutions of a Hessian equation
From MaRDI portal
Publication:1401477
DOI10.1007/s00222-002-0259-2zbMath1213.35213OpenAlexW2018071646MaRDI QIDQ1401477
Publication date: 17 August 2003
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00222-002-0259-2
Related Items (only showing first 100 items - show all)
Curvature estimates for spacelike graphic hypersurfaces in Lorentz–Minkowski space R1n+1$\mathbb {R}^{n+1}_{1}$ ⋮ Hypersurfaces of prescribed mixed Weingarten curvature ⋮ Characterizations of the viscosity solution of a nonlocal and nonlinear equation induced by the fractional \(p\)-Laplace and the fractional \(p\)-convexity ⋮ Interior curvature bounds for a type of mixed Hessian quotient equations ⋮ A weighted gradient estimate for solutions of \(L^p\) Christoffel-Minkowski problem ⋮ Prescribed \(L_p\) curvature problem ⋮ A note on a formal Riemannian structure on conformal classes ⋮ Christoffel-Minkowski flows ⋮ Asymptotic convergence for a class of anisotropic curvature flows ⋮ Projection functions, area measures and the Alesker-Fourier transform ⋮ Mirror symmetric solutions to the centro-affine Minkowski problem ⋮ The \(L_{p}\)-Minkowski problem for \(-n < p < 1\) ⋮ A class of inverse curvature flows and 𝐿^{𝑝} dual Christoffel-Minkowski problem ⋮ The \(L_p\) dual Minkowski problem about \(0 < p < 1\) and \(q > 0\) ⋮ Deforming a hypersurface by principal radii of curvature and support function ⋮ LOCAL GRADIENT ESTIMATES FOR QUOTIENT EQUATIONS IN CONFORMAL GEOMETRY ⋮ A uniqueness theorem in Kähler geometry ⋮ Existence and uniqueness of solutions to the Orlicz Aleksandrov problem ⋮ A Brunn-Minkowski inequality for the Hessian eigenvalue in three-dimensional convex domain ⋮ A new proof of gradient estimates for mean curvature equations with oblique boundary conditions ⋮ On a constant rank theorem for nonlinear elliptic PDEs ⋮ The Christoffel-Minkowski problem. II: Weingarten curvature equations ⋮ On the planar dual Minkowski problem ⋮ A microscopic convexity principle for nonlinear partial differential equations ⋮ Local solvability of the \(k\)-Hessian equations ⋮ A Hopf theorem for non-constant mean curvature and a conjecture of A. D. Alexandrov ⋮ A sharp height estimate for the spacelike constant mean curvature graph in the Lorentz-Minkowski space ⋮ Optimal concavity of some Hessian operators and the prescribed \(\sigma_2\) curvature measure problem ⋮ Convexity of level lines of maximal space-like hypersurfaces in Minkowski space ⋮ Constant rank theorems for Li-Yau-Hamilton type matrices of heat equations ⋮ An extremal case of the equation of prescribed Weingarten curvature ⋮ Curvature estimates of hypersurfaces in the Minkowski space ⋮ A flow method for a generalization of \(L_p\) Christofell-Minkowski problem ⋮ Power convexity of a class of elliptic equations involving the Hessian operator in a 3-dimensional bounded convex domain ⋮ The Hadamard variational formula and the Minkowski problem for \(p\)-capacity ⋮ Deforming a convex hypersurface by anisotropic curvature flows ⋮ Second order estimates for Hessian type fully nonlinear elliptic equations on Riemannian manifolds ⋮ A microscopic convexity theorem of level sets for solutions to elliptic equations ⋮ Reconstruction problems of convex bodies from surface area measures and lightness functions ⋮ Existence of non-symmetric solutions to the Gaussian Minkowski problem ⋮ Flow by 𝜎_{𝑘} curvature to the Orlicz Christoffel-Minkowski problem ⋮ Uniqueness of solutions to a class of mixed Hessian quotient type equations ⋮ Uniqueness of solutions to \(L_p\)-Christoffel-Minkowski problem for \(p < 1\) ⋮ Constant rank theorems for curvature problems via a viscosity approach ⋮ \textit{A priori} bounds, existence, and uniqueness of smooth solutions to an anisotropic \(L_p\) Minkowski problem for log-concave measure ⋮ A curvature flow approach to \(L^p\) Christoffel-Minkowski problem for \(1<p<k+1\) ⋮ Prescribed curvature measure problem in hyperbolic space ⋮ The \(L_p\) chord Minkowski problem ⋮ Boundary regularity for \(k\)-Hessian equations ⋮ A constant rank theorem for spacetime convex solutions of heat equation ⋮ Power convexity of solutions to a special Lagrangian equation in dimension two ⋮ A microscopic convexity principle for spacetime convex solutions of fully nonlinear parabolic equations ⋮ The existence of \(k\)-convex hypersurface with prescribed mean curvature ⋮ Existence and convexity of local solutions to degenerate Hessian equations ⋮ Weak Harnack inequalities for eigenvalues and a constant rank theorem for level sets ⋮ Hypersurfaces of prescribed curvature measure ⋮ Unnamed Item ⋮ A note on closed convex hypersurfaces with singularities ⋮ The \(L_p\) Minkowski problem for the electrostatic \(\mathfrak{p}\)-capacity ⋮ On Space-Time Quasiconcave Solutions of the Heat Equation ⋮ Isoperimetric type problems and Alexandrov-Fenchel type inequalities in the hyperbolic space ⋮ Characterization of ellipsoids through an overdetermined boundary value problem of Monge-Ampère type ⋮ A \(L_p\) Brunn-Minkowski theory for logarithmic capacity ⋮ On the microscopic spacetime convexity principle of fully nonlinear parabolic equations. I: Spacetime convex solutions ⋮ Curvature estimates for the level sets of spatial quasiconcave solutions to a class of parabolic equations ⋮ Some Liouville type results of Hessian equations ⋮ Orlicz-Minkowski flows ⋮ Uniqueness of closed self-similar solutions to \(\sigma_k^\alpha\)-curvature flow ⋮ Convexity of solutions and Brunn-Minkowski inequalities for Hessian equations in \(\mathbb{R}^3\) ⋮ The Neumann problem for parabolic Hessian quotient equations ⋮ Curvature Measures, Isoperimetric Type Inequalities and Fully Nonlinear PDEs ⋮ On a class of fully nonlinear flows in Kähler geometry ⋮ The Dirichlet problem for Hessian type elliptic equations on Riemannian manifolds ⋮ The logarithmic Minkowski problem for non-symmetric measures ⋮ A class of anisotropic expanding curvature flows ⋮ The convexity of solution of a class Hessian equation in bounded convex domain in \(\mathbb R^3\) ⋮ Convexity of level sets of minimal graph on space form with nonnegative curvature ⋮ Starshaped compact hypersurfaces with prescribed Weingarten curvature in warped product manifolds ⋮ \(L^p\) Christoffel-Minkowski problem: the case \(1< p<k+1\) ⋮ Parabolic approaches to curvature equations ⋮ Convex hypersurfaces with prescribed scalar curvature and asymptotic boundary in hyperbolic space ⋮ Weak Harnack inequalities for eigenvalues and constant rank theorems ⋮ The logarithmic Minkowski problem for polytopes ⋮ The logarithmic Minkowski problem ⋮ On the \(L_{p}\) Monge-Ampère equation ⋮ On the planar \(L_p\)-Minkowski problem ⋮ Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems ⋮ The Christoffel problem by the fundamental solution of the Laplace equation ⋮ The planar \(L_p\) dual Minkowski problem ⋮ Volume preserving flow and Alexandrov-Fenchel type inequalities in hyperbolic space ⋮ A fully nonlinear partial differential equation and its application to the \(\sigma_k\)-Yamabe problem ⋮ Inclusion relations of Gårding's cones and \(k\)-convex cones ⋮ The \(L_p\) Minkowski problem for torsion ⋮ Boundary Hölder regularity for a class of fully nonlinear elliptic partial differential equations ⋮ A Fourier transform approach to Christoffel’s problem ⋮ Weak solutions to the complex Hessian equation. ⋮ The Lp Minkowski problem for q-capacity ⋮ Convexity estimates for the solutions of a class of semi-linear elliptic equations ⋮ Uniqueness of solutions to the logarithmic Minkowski problem in \(\mathbb{R}^3\) ⋮ The \(L_p\) Minkowski type problem for a class of mixed Hessian quotient equations
This page was built for publication: The Christoffel-Minkowski problem. I: Convexity of solutions of a Hessian equation