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math.DG2023★ 2 cited
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…
math.DG2020
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…
math.DG2018
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…