相关论文: Curvature estimates for a class of Hessian type eq…

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 applications for our estimate.

The main result of this paper gives a plenary proof on the curvature estimates for $k$ curvature equations with general right hand sides with $n<2k$ based on a concavity inequality. We further give a explicit lower bound of the inequality.

We give some estimate of type sup*inf for scalar curvature type equations.

In this paper, we establish a curvature estimate for semi-convex solutions of Hessian equations in hyperbolic space. We also obtain a curvature estimate for admissible solutions to prescribed curvature measure type problem in hyperbolic…

We derive Hessian estimates for convex solutions to quadratic Hessian equation by a compactness argument.

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.

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 possessing curvature estimates. In this paper, we discuss…

We prove estimates for the sectional curvature of hyperkaehler quotients and give applications to moduli spaces of solutions to Nahm's equations and Hitchin's equations.

We are concerned with the Dirichlet problem for a class of Hessian type equations. Applying some new methods we are able to establish the $C^2$ estimates for an approximating problem under essentially optimal structure conditions. Based on…

In this paper, we mainly study the interior $C^2$ estimates for a class of sum Hessian equations. We establish the interior estimates and the Pogorelov type estimates for $0<k<n$. If $k=n$, we derive a weaker Pogorelov type estimates.

In [Amer. J. Math. 141 (2019), no. 5, 1281-1315], Ren and Wang proved the curvature estimates for the $n-1$ curvature equation. The purpose of this note is to give a simple proof of their theorem.

In this paper, we consider a Class of Hessian quotient equations in Euclidean space. Under some sufficient condition, we obtain an existence result by the standard degree theory based on the a prior estimates for the solutions to the…

In this paper, we derive a priori interior Hessian estimates for Lagrangian mean curvature equation if the Lagrangian phase is supercritical and has bounded second derivatives.

In this paper, we consider a class of prescribed Weingarten curvature equations. Under some sufficient condition, we obtain an existence result by the standard degree theory based on the a prior estimates for the solutions to the prescribed…

In this paper, we study Hessian equations with prescribed contact angle boundary value or oblique derivative boundary value and finally derive the a priori global gradient estimate for the admissible solutions.

In this paper, we study the interior gradient estimates for admissible solutions to prescribed curvature equations in hyperbolic space.

We give a uniform estimate for solutions of prescribed scalar curvature type equation in dimension 4.

We establish the Pogorelov type estimates for degenerate prescribed k-curvature equations as well as k-Hessian equations. Furthermore,we investigate the interior C1,1 regularity of the solutions for Dirichlet problems. These techniques also…

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 $k$-convex solutions and admissible solutions under some…

We give a relationship that yields an effective geometric way of evaluating mean curvature of surfaces. The approach is reminiscent of the Gauss's contour based evaluation of intrinsic curvature. The presented formula may have a number of…