The Bernstein problem for affine maximal hypersurfaces
From MaRDI portal
Publication:1568824
DOI10.1007/s002220000059zbMath0978.53021OpenAlexW1988312779MaRDI QIDQ1568824
Xu-Jia Wang, Neil S. Trudinger
Publication date: 7 February 2002
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s002220000059
affine completenessBernstein problemequiaffine mean curvatureaffine maximal hypersurfaceuniform strict convexity
Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Nonlinear elliptic equations (35J60) Affine differential geometry (53A15)
Related Items
Enclosed convex hypersurfaces with maximal affine area, Solvability of a class of singular fourth order equations of Monge-Ampère type, Global \(W^{2,p}\) regularity on the linearized Monge-Ampère equation with \(\text{VMO}\) Type coefficients, Centroaffine Bernstein problems, The exterior Dirichlet problems of Monge-Ampère equations in dimension two, \(C^{1}\) regularity of solutions of the Monge-Ampère equation for optimal transport in dimension two, Variational solutions to extremal metrics on toric surfaces, \(W^{4, p}\) solution to the second boundary value problem of the prescribed affine mean curvature and Abreu's equations, A Bernstein property of solutions to a class of prescribed affine mean curvature equations, Necessary and sufficient conditions on the existence of solutions for the exterior Dirichlet problem of Hessian equations, Centro–affine curvature flows on centrally symmetric convex curves, A Bernstein theorem for the Abreu equation, On certain degenerate and singular elliptic PDEs. III: Nondivergence form operators and \(RH_\infty\)-weights, On the exterior Dirichlet problem for Hessian equations, Unnamed Item, The Monge–Ampère equation and its link to optimal transportation, Harnack inequality for the fractional nonlocal linearized Monge-Ampère equation, Global \(W^{1,p}\) estimates for solutions to the linearized Monge-Ampère equations, Monge-Ampère Equation with Bounded Periodic Data, On certain degenerate and singular elliptic PDEs I: nondivergence form operators with unbounded drifts and applications to subelliptic equations, The exterior Dirichlet problem for special Lagrangian equations in dimensions \(n\leq 4\), Interior estimates for the Monge-Ampère type fourth order equations, A Bernstein type theorem for entire Willmore graphs, Bernstein problem of affine maximal type hypersurfaces on dimension \(N \geq 3\), A Liouville theorem for the Neumann problem of Monge-Ampère equations, Floating functions, The Solutions with Prescribed Asymptotic Behavior for the Exterior Dirichlet Problem of Hessian Equations, The maximal curves and heat flow in general-affine geometry, Ulam floating functions, Interior regularity on the Abreu equation, Solutions of some Monge-Ampère equations with isolated and line singularities, Equiaffine geometry of level sets and ruled hypersurfaces with equiaffine mean curvature zero, The exterior Dirichlet problem for Hessian quotient equations, Geometric structures as determined by the volume of generalized geodesic balls, A Bernstein property of certain types of fourth order partial differential equations, Boundary regularity for solutions to the linearized Monge-Ampère equations, On the exterior Dirichlet problem for Hessian quotient equations, Convex solutions to the mean curvature flow, The exterior Dirichlet problem for fully nonlinear elliptic equations related to the eigenvalues of the Hessian, The global existence and convergence of the Calabi flow on \(\mathbb C^{n}/\mathbb Z^{n}+i \mathbb Z^{n}\), Interior gradient estimates for solutions to the linearized Monge-Ampère equation, A Bernstein theorem for affine maximal-type hypersurfaces, A Liouville theorem for solutions of the Monge--Ampère equation with periodic data., Global \(W^{2,p}\) estimates for solutions to the linearized Monge-Ampère equations, Minimizing weak solutions for Calabi's extremal metrics on toric manifolds, On the stability of the \(p\)-affine isoperimetric inequality, The Bernstein theorem for a class of fourth order equations, The Monge-Ampère equation with Guillemin boundary conditions, The interior regularity of the Calabi flow on a toric surface, Interior estimates for solutions of a fourth order nonlinear partial differential equation, The indefinite affine Cauchy problem, A Bernstein property for F relative parabolic affine hyperspheres, On Monge–Ampère Type Equations and Applications, Necessary and sufficient conditions on existence and convexity of solutions for Dirichlet problems of Hessian equations on exterior domains, A Liouville Theorem for Solutions of Degenerate Monge-Ampère Equations, \(\mathrm{SL}(n)\) invariant valuations on polytopes, Notes on Chern's affine Bernstein conjecture, An extension of the affine Bernstein problem, On the exterior Dirichlet problem for Monge-Ampère equations, On the extension of Calabi flow on toric varieties, Bernstein properties for \(\alpha\)-complete hypersurfaces, The affine Plateau problem, A Bernstein type theorem for minimal volume preserving maps, On the exterior Dirichlet problem for the Monge-Ampère equation in dimension two, General affine surface areas, A Bernstein theorem for affine maximal type hypersurfaces under decaying convexity, Approximation of variational problems with a convexity constraint by PDEs of Abreu type, The Calabi conjecture on affine maximal surfaces, Existence and nonexistence to exterior Dirichlet problem for Monge-Ampère equation, An extension to a theorem of Jörgens, Calabi, and Pogorelov, Rigidity theorems for the entire solutions of 2-Hessian equation, On the rigidity theorems for entire Lagrangian translating solitons in pseudo-Euclidean space IV, Interior \(C^{1,\alpha}\) regularity for the linearized Monge-Ampère equation with VMO type coefficients, The Bernstein problem for affine maximal type hypersurfaces under decaying convexity, The affine Cauchy problem, On approximating minimizers of convex functionals with a convexity constraint by singular Abreu equations without uniform convexity, Global Hölder estimates for 2D linearized Monge-Ampère equations with right-hand side in divergence form, A mean-value inequality for non-negative solutions to the linearized Monge-Ampère equation, Non-removable singularities of a fourth-order nonlinear partial differential equation, An optimal transport approach to Monge-Ampère equations on compact Hessian manifolds, Interior second derivative estimates for solutions to the linearized Monge-Ampère equation, 𝑊^{{}2,𝑝}–estimates for the linearized Monge–Ampère equation, On the entire self-shrinking solutions to Lagrangian mean curvature flow. II., The space of solutions to the Hessian one equation in the finitely punctured plane, Boundary Harnack inequality for the linearized Monge-Ampère equations and applications
