Search
Search Results
-
Serrin-Type Overdetermined Problems for Hessian Quotient Equations and Hessian Quotient Curvature Equations
We consider overdetermined problems for Hessian quotient equations and Hessian quotient curvature equations, which are fully nonlinear elliptic...
-
Boundary Regularity for k-Hessian Equations
In this paper we focus on the boundary regularity for a class of k -Hessian equations which can be degenerate and (or) singular on the boundary of the...
-
The weak solutions to complex Hessian equations
In this paper, we shall study existence of weak solutions to complex Hessian equations on compact Hermitian manifolds. With appropriate assumptions,...
-
Trace inequalities, isocapacitary inequalities, and regularity of the complex Hessian equations
In this paper, we study the relations between trace inequalities (Sobolev and Moser-Trudinger types), isocapacitary inequalities, and the regularity...
-
On the Hessian-cscK equations
In this paper, we propose a coupled system of complex Hessian equations which generalizes the equation for constant scalar curvature Kähler (cscK)...
-
Curvature estimates for a class of Hessian quotient type curvature equations
In this paper, we are concerned with the hypersurface that can be locally represented as a graph and satisfies a class of Hessian quotient type...
-
Stability estimates for the complex Monge-Ampère and Hessian equations
A new proof for stability estimates for the complex Monge-Ampère and Hessian equations is given, which does not require pluripotential theory. A...
-
Hessian Equations of Krylov Type on Kähler Manifolds
In this paper, we consider a Hessian equation with its structure as a combination of elementary symmetric functions on closed Kähler manifolds. We...
-
Curvature estimates for semi-convex solutions of Hessian equations in hyperbolic space
In this paper, we establish a curvature estimate for semi-convex solutions of Hessian equations in hyperbolic space. We also obtain a curvature...
-
Geometry of m-Hessian Equations
In the process of develo** the modern theory of fully nonlinear, second-order partial differential equations, new geometric characteristics of...
-
Complex Hessian-Type Equations in the Weighted m-Subharmonic Class
We study the existence of a solution to a general type of complex Hessian equation on some Cegrell classes. For a given measure μ defined on an m -hype...
-
The existence of radial k-admissible solutions for n-dimension system of k-Hessian equations
In this paper, we focus on a general n -dimension system of k -Hessian equations. By introducing some new suitable growth conditions, the existence...
-
Gårding Cones and Bellman Equations in the Theory of Hessian Operators and Equations
In this work, we continue the investigation of algebraic properties of Gårding cones in the space of symmetric matrices. Based on this theory, we...
-
The Neumann Problem for Parabolic Hessian Quotient Equations
In this paper, we consider the Neumann problem for parabolic Hessian quotient equations. We show that the k -admissible solution of the parabolic...
-
The Second Hessian Type Equation on Almost Hermitian Manifolds
In this paper, we derive the second order estimate to the 2nd Hessian type equation on a compact almost Hermitian manifold.
-
Liouville type theorems and Hessian estimates for special Lagrangian equations
In this paper, we get a Liouville type theorem for the special Lagrangian equation with a certain ’convexity’ condition, where Warren–Yuan first...
-
Interior Hessian Estimates for σ2 Equations in Dimension Three
We prove a priori interior C 2 estimate for σ 2 = f in ℝ 3 , which generalizes Warren–Yuan’s result [Comm. Pure Appl. Math., 2009, 62(3): 305–321].