4 papers
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 general sum-type Hessian equations
Weisong Dong, Sirui Xu, Ruijia Zhang
In this paper, we exploit the concavity of sums of Hessian operators to derive Pogorelov estimates for corresponding equations under the dynamic semi-convexity assumption, and we f…
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,…