28 citations · 58 across the 12 of their papers we have counts for
13 papers
Curvature estimates for semi-convex solutions of Hessian equations in hyperbolic space
Siyuan Lu
In this paper, we establish a curvature estimate for semi-convex solutions of Hessian equations in hyperbolic space. We also obtain a curvature estimate for admissible solutions to…
On the asymptotic Plateau problem in hyperbolic space
Siyuan Lu
In this paper, we solve the asymptotic Plateau problem in hyperbolic space for constant curvature, i.e. the existence of a complete hypersurface in sat…
On the Dirichlet problem for Lagrangian phase equation with critical and supercritical phase
Siyuan Lu
In this paper, we solve the Dirichlet problem for Lagrangian phase equation with critical and supercritical phase. A crucial ingredient is the interior estimate. Our result i…
On the -Nirenberg problem on
YanYan Li, Han Lu, Siyuan Lu
We establish theorems on the existence and compactness of solutions to the -Nirenberg problem on the standard sphere . A first significant ingredient, a Liouville…
A Liouville theorem for Möbius invariant equations
YanYan Li, Han Lu, Siyuan Lu
In this paper we classify Möbius invariant differential operators of second order in two dimensional Euclidean space, and establish a Liouville type theorem for general Möbius inva…
Rigidity of Riemannian Penrose inequality with corners and its implications
Siyuan Lu, Pengzi Miao
Motivated by the rigidity case in the localized Riemannian Penrose inequality, we show that suitable singular metrics attaining the optimal value in the Riemannian Penrose inequali…
Monge-Ampère equation with bounded periodic data
YanYan Li, Siyuan Lu
We consider the Monge-Ampère equation in , where is a positive bounded periodic function. We prove that must be the sum of a quadratic polynomi…
Variation and rigidity of quasi-local mass
Siyuan Lu, Pengzi Miao
Inspired by the work of Chen-Zhang \cite{Chen-Zhang}, we derive an evolution formula for the Wang-Yau quasi-local energy in reference to a static space, introduced by Chen-Wang-Wan…
Existence and nonexistence to exterior Dirichlet problem For Monge-Ampère equation
Yanyan Li, Siyuan Lu
We consider the exterior Dirichlet problem for Monge-Ampère equation with prescribed asymptotic behavior. Based on earlier work by Caffarelli and the first named author, we complet…
Minimal hypersurfaces and boundary behavior of compact manifolds with nonnegative scalar curvature
Siyuan Lu, Pengzi Miao
On a compact Riemannian manifold with boundary having positive mean curvature, a fundamental result of Shi and Tam states that, if the manifold has nonnegative scalar curvature and…
Inverse curvature flow in anti-de Sitter-Schwarzschild manifold
Siyuan Lu
In this paper, we consider the inverse hessian quotient curvature flow with star-shaped initial hypersurface in anti-de Sitter-Schwarzschild manifold. We prove that the solution ex…
On Weyl's embedding problem in Riemannian manifolds
Siyuan Lu
We consider a priori estimates of Weyl's embedding problem of in general -dimensional Riemannian manifold . We establish interior estima…
Curvature estimates for immersed hypersurfaces in Riemannian manifolds
Pengfei Guan, Siyuan Lu
We establish mean curvature estimate for immersed hypersurface with nonnegative extrinsic scalar curvature in Riemannian manifold through regularity study of a…