Changyu Ren

activity

20132022

C^{2}

estimates for convex solutions of curvature equations

13 citations · 36 across the 9 of their papers we have counts for

collaborators

9 papers

math.CA2022

A generalization of Newton-Maclaurin's inequalities

Changyu Ren

In this paper, we prove Newton-Maclaurin type inequalities for functions obtained by linear combination of two neighboring primary symmetry functions, which is a generalization of…

math.AP2022

Pogorelov type $C^{2}$ estimates for Sum Hessian equations and a rigidity theorem

Yue Liu, Changyu Ren

We mainly study Pogorelov type $C^{2}$ estimates for solutions to the Dirichlet problem of Sum Hessian equations. We establish respectively Pogorelov type $C^{2}$ estimates for $k$ -con…

math.DG2020★ 6 cited

The prescribed curvature problem for entire hypersurfaces in Minkowski space

Changyu Ren, Zhizhang Wang, Ling Xiao

We prove three results in this paper. First, we prove for a wide class of functions $φ \in C^{2} (S^{n - 1})$ and $ψ (X, ν) \in C^{2} (R^{n + 1} \times H^{n}),$ there exi…

math.AP2020★ 2 cited

Notes on the curvature estimates for Hessian equations

Changyu Ren, Zhizhang Wang

The main result of this paper gives a plenary proof on the curvature estimates for $k$ curvature equations with general right hand sides with $n < 2 k$ based on a concavity inequality…

math.AP2020★ 6 cited

The global curvature estimate for the n-2 Hessian equation

Changyu Ren, Zhizhang Wang

This paper establishes the global curvature estimate for the $n - 2$ curvature equation with the general right hand side which partially solves this longstanding problem.

math.AP2017★ 2 cited

The curvature estimates for convex solutions of some fully nonlinear Hessian type equations

Chunhe Li, Changyu Ren, Zhizhang Wang

The curvature estimates of quotient curvature equation do not always exist even for convex setting \cite{GRW}. Thus it is natural question to find other type of elliptic equations…

math.AP2016★ 3 cited

On the curvature estimates for Hessian equations

Changyu Ren, Zhizhang Wang

The curvature estimates of $k$ curvature equations for general right hand side is a longstanding problem. In this paper, we totally solve the $n - 1$ case and we also discuss some ap…

math.AP2015★ 4 cited

An interior estimate for convex solutions and a rigidity theorem

MIng Li, Changyu Ren, Zhizhang Wang

We establish an interior $C^{2}$ estimate for $k + 1$ convex solutions to Dirichlet problems of $k$ -Hessian equations. We also use such estimate to obtain a rigidity theorem for $k + 1$ …

math.AP2013★ 13 cited

Global $C^{2}$ estimates for convex solutions of curvature equations

Pengfei Guan, Changyu Ren, Zhizhang Wang

We establish $C^{2}$ a priori estimate for convex hypersurfaces whose principal curvatures $κ = (κ_{1}, ..., κ_{n})$ satisfying Weingarten curvature equation $σ_{k} (κ (X)) = f (X, ν (X))$ . We also…

A generalization of Newton-Maclaurin's inequalities

Pogorelov type C2 estimates for Sum Hessian equations and a rigidity theorem

The prescribed curvature problem for entire hypersurfaces in Minkowski space

Notes on the curvature estimates for Hessian equations

The global curvature estimate for the n-2 Hessian equation

The curvature estimates for convex solutions of some fully nonlinear Hessian type equations

On the curvature estimates for Hessian equations

An interior estimate for convex solutions and a rigidity theorem

Global C2 estimates for convex solutions of curvature equations

Pogorelov type $C^{2}$ estimates for Sum Hessian equations and a rigidity theorem

Global $C^{2}$ estimates for convex solutions of curvature equations