31 citations · 46 across the 14 of their papers we have counts for
14 papers
Concavity Properties of Robin Solutions on Uniformly Convex Domains
Dong Ye, Dekai Zhang
We prove that, on a bounded uniformly convex domain of class , the first Robin eigenfunction is strictly log-concave and the Robin torsion function is strictly -conca…
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…
Serrin-type overdetermined problems for Hessian quotient equations
Zhenghuan Gao, Xiaohan Jia, Dekai Zhang
We prove the symmetry of solutions to overdetermined problems for a class of fully nonlinear equations, namely Hessian quotient equations and Hessian quotient curvature equations.…
The exterior Dirichlet Problem for homogeneous complex -Hessian equation
Zhenghuan Gao, Xi-Nan Ma, Dekai Zhang
In this paper, we consider the homogeneous complex k-Hessian equation in an exterior domain . We prove the existence and uniqueness of the solutio…
A Federated Cox Model with Non-Proportional Hazards
Dekai Zhang, Francesca Toni, Matthew Williams
Recent research has shown the potential for neural networks to improve upon classical survival models such as the Cox model, which is widely used in clinical practice. Neural netwo…
The exterior Dirichlet problem for the homogeneous -Hessian equation
Xi-Nan Ma, Dekai Zhang
We study the exterior Dirichlet problem for the homogeneous -Hessian equation. The prescribed asymptotic behavior at infinity of the solution is zero if , it is $…
A new flow solving the LYZ equation in Kähler geometry
Jixiang Fu, Shing-Tung Yau, Dekai Zhang
We introduced a new flow to the LYZ equation on a compact Kähler manifold. We first show the existence of the longtime solution of the flow. We then show that under the Collins-Jac…
The Neumann problem of Hessian quotient equations
Chuanqiang Chen, Dekai Zhang
In this paper, we obtain some important inequalities of Hessian quotient operators, and global estimates of the Neumann problem of Hessian quotient equations. By the method o…
The Neumann Problem for Parabolic Hessian Quotient Equations
Chuanqiang Chen, Xi-Nan Ma, Dekai Zhang
In this paper, we consider the Neumann problem for parabolic Hessian quotient equations. We show that the -admissible solution of the parabolic Hessian quotient equation exists…
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…
Gradient Estimates of Mean Curvature Equation with Neumann Boundary Condition in
Jinju Xu, Dekai Zhang
In this note, we study the prescribed mean curvature equation with Neumann boundary conditions on Riemannian product manifold . The main goal is to establish…
Hessian equations on closed Hermitian manifolds
Dekai Zhang
In this paper, using the technical tools in \cite{TW5}, we solve the complex Hessian equation on closed Hermitian manifolds, which generalizes the the Kähler case results in \cite{…