A class of curvature type equation

DOI10.4310/PAMQ.2021.v17.n3.a2MaRDI QIDQ2031889

Xiangwen Zhang, Pengfei Guan

Publication date: 15 June 2021

Published in: Pure and Applied Mathematics Quarterly (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.03645

zbMATH Keywords

Dirichlet problem\(C^{1,1}\) estimatesChristoffel-Minkowski problemcurvature equations

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Elliptic equations on manifolds, general theory (58J05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45)

Related Items (21)

The Dirichlet problem for degenerate curvature equations ⋮ A type of parabolic flow with mixed hessians on compact Kähler manifolds ⋮ The Neumann problem for a class of mixed complex Hessian equations ⋮ The Dirichlet problem for a class of prescribed curvature equations ⋮ Concavity of the Lagrangian phase operator and applications ⋮ Complete conformal metrics of negative Ricci curvature in open manifolds ⋮ The classical Neumann problem for a class of mixed Hessian equations ⋮ Constant rank theorems for curvature problems via a viscosity approach ⋮ On the convexity of general inverse \(\sigma_k\) equations ⋮ On fully nonlinear Loewner-Nirenberg problem of Ricci curvature ⋮ The Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds ⋮ Hessian equations of Krylov type on Kähler manifolds ⋮ Dirichlet problem for Krylov type equation in conformal geometry ⋮ Curvature estimates for \(p\)-convex hypersurfaces of prescribed curvature ⋮ Interior curvature bounds for a type of mixed Hessian quotient equations ⋮ Unnamed Item ⋮ Pogorelov estimates for a class of fully nonlinear equations ⋮ A class of the non-degenerate complex quotient equations on compact Kähler manifolds ⋮ A class of prescribed Weingarten curvature equations in Euclidean space ⋮ Pogorelov type \(C^2\) estimates for sum Hessian equations and a rigidity theorem ⋮ Hessian equations of Krylov type on compact Hermitian manifolds

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