1 citations · 1 across the 2 of their papers we have counts for
6 papers
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…