5 papers
The parabolic quaternionic Monge-Ampère type equation on hyperKähler manifolds
Jixiang Fu, Xin Xu, Dekai Zhang
We prove the long time existence and uniqueness of solution to a parabolic quaternionic Monge-Ampère type equation on a compact hyperKähler manifold. We also show that after normal…
The Dirichlet problem of homogeneous complex k-Hessian equation in a (k-1)-pesudoconvex domain with isolated singularity
Zhenghuan Gao, Xi-Nan Ma, Dekai Zhang
In this paper, we consider the homogeneous complex k-Hessian equation in . We prove the existence and uniqueness of the solution by constructing approxi…
The Dirichlet problem of the homogeneous -Hessian equation in a punctured domain
Zhenghuan Gao, Xi-Nan Ma, Dekai Zhang
In this paper, we consider the Dirichlet problem for the homogeneous -Hessian equation with prescribed asymptotic behavior at where is a -convex bounded domai…
The Monge-Ampère equation for -quaternionic PSH functions on a hyperKähler manifold
Jixiang Fu, Xin Xu, Dekai Zhang
We prove the existence of unique smooth solutions to the quaternionic Monge-Ampère equation for -quaternionic plurisubharmonic functions on a hyperKähler manifold and thus o…
Convexity of Level Sets of Minimal Graph on Space Form with Nonnegative Curvature
Peihe Wang, Dekai Zhang
For the minimal graph defined on a convex ring in the space form with nonnegative curvature, we obtain the regularity and the strict convexity about its level sets by the continuit…