7 papers
Interior Hessian estimates for Hessian quotient equations in dimension three
Heming Jiao, Zhenan Sui
In this paper, we establish the interior Hessian estimates for -convex solutions to in dimension three. In higher dimensions (), we…
Asymptotic Plateau problem for -convex hypersurface in
Zhenan Sui
We prove the existence of a smooth complete -convex hypersurface which satisfies prescribed curvature equation for $n…
Existence of solution to modified Gursky-Streets equation
Yi Huang, Zhenan Sui, Mingyu Xie
We solve the modified Gursky-Streets equation, which is a fully nonlinear equation arising in conformal geometry with uniform estimates when (i) and $1 \leq k \le…
Lipschitz Continuous Hypersurfaces with Prescribed Curvature and Asymptotic Boundary in Hyperbolic Space
Zhenan Sui, Wei Sun
We prove the existence of a complete locally Lipschitz continuous hypersurface in weak sense with prescribed Weingarten curvature and asymptotic boundary at infinity in hyperbolic…
Convex Hypersurfaces with Prescribed Scalar Curvature and Asymptotic Boundary in Hyperbolic Space
Zhenan Sui
The existence of a smooth complete strictly locally convex hypersurface with prescribed scalar curvature and asymptotic boundary at infinity in is proved under the…
Strictly Locally Convex Radial Graphs of Prescribed Curvature and Boundary in Space Forms
Zhenan Sui
We obtain a priori estimates for solutions of the nonlinear second-order elliptic equation related to the geometric problem of finding a strictly locally convex hypersurface…