6 papers
Interior Hessian estimates for Hessian quotient equations
Weisong Dong, Ruijia Zhang
In this paper, we establish interior estimates for admissible semiconvex solutions to the general Hessian quotient equation for the cases $l=k…
Second order estimates for equations with sums of Hessian operators on Hermitian manifolds
Weisong Dong, Ruijia Zhang
In this paper, we establish an a priori second-order estimate for admissible solutions satisfying a dynamic plurisubharmonic condition to equations involving sums of Hessian operat…
Pogorelov interior estimates for sum-of-Hessians equations
Weisong Dong, Sirui Xu, Ruijia Zhang
In this paper, we develop a new approach to sum-of-Hessians equations involving multiple -Hessian operators of distinct orders. By exploiting the concavity of sums of Hessian op…
A Liouville-type theorem for -Monge-Ampère equation in dimension three
Weisong Dong
We prove that every entire solution with quadratic growth, lying in a suitable cone, to the 2-Monge-Ampère equation on is a quadratic polynomial. The proof proceeds…
Boundary estimates for a fully nonlinear Yamabe problem on Riemannian manifolds
Weisong Dong, Yanyan Li, Luc Nguyen
In this paper, we consider the Dirichlet boundary value problem for fully nonlinear Yamabe equations on Riemannian manifolds with boundary. Assuming the existence of a subsolution,…
The Dirichlet problem for Monge-Ampère type equations on Riemannian manifolds
Weisong Dong, Jinling Niu, Nadilamu Nizhamuding
In this paper, we study the Dirichlet problem for Monge-Ampère type equations for -plurisubharmonic functions on Riemannian manifolds. The estimates up to the secon…