Dekai Zhang

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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 $Ω\ {0}$ . We prove the existence and uniqueness of the $C^{1, α}$ solution by constructing approxi…

math.AP2023

The Dirichlet problem of the homogeneous $k$ -Hessian equation in a punctured domain

Zhenghuan Gao, Xi-Nan Ma, Dekai Zhang

In this paper, we consider the Dirichlet problem for the homogeneous $k$ -Hessian equation with prescribed asymptotic behavior at $0 \in Ω$ where $Ω$ is a $(k - 1)$ -convex bounded domai…

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…

The Dirichlet problem of homogeneous complex k-Hessian equation in a (k-1)-pesudoconvex domain with isolated singularity

The Dirichlet problem of the homogeneous k-Hessian equation in a punctured domain

Convexity of Level Sets of Minimal Graph on Space Form with Nonnegative Curvature

The Dirichlet problem of the homogeneous $k$ -Hessian equation in a punctured domain