32 citations · 78 across the 15 of their papers we have counts for
16 papers
Brunn--Minkowski Inequality for the First Complex -Hessian Eigenvalue
Chuanqiang Chen, Jiahuan Li, Xi-Nan Ma
There are relatively few results on the convexity of solutions to complex equations. In this paper, We prove a strict real log-concavity theorem for the first eigenfunction of the…
A fully-nonlinear flow and quermassintegral inequalities in the sphere
Chuanqiang Chen, Pengfei Guan, Junfang Li +1
This expository paper presents the current knowledge of particular fully nonlinear curvature flows with local forcing term, so-called locally constrained curvature flows. We focus…
The Neumann problem of Hessian quotient equations
Chuanqiang Chen, Dekai Zhang
In this paper, we obtain some important inequalities of Hessian quotient operators, and global estimates of the Neumann problem of Hessian quotient equations. By the method o…
The Neumann problem for a class of mixed complex Hessian equations
Chuan-Qiang Chen, Li Chen, Ni Xiang
In this paper, we consider the Neumann problem of a class of mixed complex Hessian equations, and establish the global C^1 estimates a nd reduce the global second derivative estima…
The classical Neumann problem for a class of mixed Hessian equations
Chuan-Qiang Chen, Li Chen, Ni Xiang
In this paper, we establish global C^2 estimates for a class of mixed Hessian equations with Neumann boundary condition, and obtain the existence theorem of k-admissible solutions…
Neumann problem for a class of fully nonlinear equations
Chuan-Qiang Chen, Li Chen, Ni Xiang
In this paper, we establish a priori estimates for a class of fully nonlinear equations with Neumann boundary conditions. By the continuity method, we have obtained the existence t…
The Neumann Problem for Parabolic Hessian Quotient Equations
Chuanqiang Chen, Xi-Nan Ma, Dekai Zhang
In this paper, we consider the Neumann problem for parabolic Hessian quotient equations. We show that the -admissible solution of the parabolic Hessian quotient equation exists…
The interior estimate for prescribed Gauss curvature equation in dimension two
Chuanqiang Chen, Fei Han, Qianzhong Ou
In this paper, we introduce a new auxiliary function, and establish the interior estimate for prescribed Gauss curvature equation in dimension two.
The interior estimate for Monge-Ampere equation in dimension
Chuanqiang Chen, Fei Han, Qianzhong Ou
In this paper, we introduce a new auxiliary function, and establish the interior estimate for Monge-Ampere equation in dimension , which was firstly proved by Heinz \ci…
On space-time quasiconcave solutions of the heat equation
Chuanqiang Chen, Xi-Nan Ma, Paolo Salani
In this paper we first obtain a constant rank theorem for the second fundamental form of the space-time level sets of a space-time quasiconcave solution of the heat equation. Utili…
On the microscopic spacetime convexity principle of fully nonlinear parabolic equations II: Spacetime quasiconcave solutions
Chuanqiang Chen
In \cite{CMS}, Chen-Ma-Salani established the strict convexity of spacetime level sets of solutions to heat equation in convex rings, using the constant rank theorem and a deformat…
On the microscopic spacetime convexity principle for fully nonlinear parabolic equations I: Spacetime convex solutions
Chuanqiang Chen
Spacetime convexity is a basic geometric property of the solutions of parabolic equations. In this paper, we study microscopic convexity properties of spacetime convex solutions of…
Curvature estimates for the level sets of solutions of the Monge-Ampère equation
Chuanqiang Chen, Xi-Nan Ma, Shujun Shi
For the Monge-Ampère equation , we find new auxiliary curvature functions which attain respective maximum on the boundary. Moreover, we obtain the upper bounded estim…
A Minimal Value Problem and the Prescribed Curvature Measure Problem
Chuanqiang Chen
In this paper, we consider a minimal value problem and obtain an algebraic inequality. As an application, we prove the a priori estimate for a class of prescribed curva…
Curvature estimates for the level set of spatial quasiconcave solutions to a class of parabolic equations
Chuanqiang Chen, Shujun Shi
We prove a constant rank theorem for the second fundamental form of the spatial convex level surfaces of solutions to equations $u_t=F(\n^2u, \n u, u, t)$ under a structural condit…
A constant rank theorem for partial convex solutions of partial differential equations
Chuanqiang Chen
Thanks to the test function of Bian-Guan[2], we successfully obtain a constant rank theorem for partial convex solutions of a class partial differential equations. This is the micr…