activity
20152026
most citedHessian equations on closed Hermitian manifolds

31 citations · 46 across the 14 of their papers we have counts for

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9 papers · 1 filter

math.AP2026

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…

math.AP2023

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…

math.AP2023

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…

math.AP2022

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.…

math.AP2022★ 4 cited

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…

math.AP2022

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 $…

math.AP2020★ 7 cited

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…

math.AP2020

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…

math.AP2016

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…