22 citations · 40 across the 12 of their papers we have counts for
16 papers
Saddle Codazzi tensor on spheres and hemisphere rigidity
Jian Ge, Mijia Lai, Yuntian Zhu
Let , , be a compact connected Riemannian manifold with smooth boundary. We ask whether must be isometric to the standard hemisphere if , $\part…
Constant Rank Theorems under Intermediate Ricci Curvature
Mijia Lai, Guoqiang Wu
We prove two constant rank theorems for the Ricci tensor in two geometric settings: manifolds with harmonic curvature and gradient Ricci solitons. In both cases, if the -interme…
The sphere is the only closed surface satisfying the fixed-width Archimedean property
Mijia Lai
Among Archimedes' many celebrated discoveries is a striking fact: the region of the unit sphere between two parallel planes, both meeting the sphere and separated by a distance …
The optimal diameter estimate for positive Yamabe metrics
Kazuo Akutagawa, Mijia Lai, Chao Li +2
In this paper, we prove the optimal diameter estimate for positive Yamabe metrics on a connected, closed manifold. It is a scalar curvature version of both classical Myers' diamete…
Rigidity of Schouten Tensor under Conformal Deformation
Mijia Lai, Guoqiang Wu
We obtain some rigidity results for metrics whose Schouten tensor is bounded from below after conformal transformations. Liang Cheng recently proved that a complete, nonflat, local…
Gelfand problem and Hemisphere rigidity
Mijia Lai, Wei Wei
We give an interpretation of the hemisphere rigidity theorem of Hang-Wang in the framework of Gelfand problem. More precisely, Hang-Wang showed that for a metric conformal to t…
A note on Hang-Wang's hemisphere rigidity theorem
Mijia Lai
Let be a compact manifold with boundary and , Hang and Wang proved that is isometric to the standard hemisphere if is convex and isom…
The Obata equation with Robin boundary condition
Xuezhang Chen, Mijia Lai, Fang Wang
We study the Obata equation with Robin boundary condition on manifolds with boundary, where . Dirichlet and Neu…
Escobar-Yamabe compactifications for Poincare-Einstein manifolds and rigidity theorems
Xuezhang Chen, Mijia Lai, Fang Wang
Let be a Poincaré-Einstein manifold which is conformally compact with conformal infinity . On the conformal compactifi…
Volume bounds of conic 2-spheres
Hao Fang, Mijia Lai
We obtain sharp volume bound for a conic 2-sphere in terms of its Gaussian curvature bound. We also give the geometric models realizing the extremal volume. In particular, when the…
On curvature pinching of conic 2-spheres
Hao Fang, Mijia Lai
We study metrics on conic 2-spheres when no Einstein metrics exist. In particular, when the curvature of a conic metric is positive, we obtain the best curvature pinching constant.…
On convergence to a football
Hao Fang, Mijia Lai
We show that spheres of positive constant curvature with () conic points converge to a sphere of positive constant curvature with two conic points (or called an (Americ…
The J-flow on Kahler surfaces: a boundary case
Hao Fang, Mijia Lai, Jian Song +1
We study the J-flow on Kahler surfaces when the Kahler class lies on the boundary of the open cone for which global smooth convergence holds, and satisfies a nonnegativity conditio…
Convergence of general inverse -flow on Kähler manifolds with Calabi Ansatz
Hao Fang, Mijia Lai
We study the convergence behavior of the general inverse -flow on Kähler manifolds with initial metrics satisfying the Calabi Ansatz. The limiting metrics can be either smooth…
On the geometric flows solving Kählerian inverse equations
Hao Fang, Mijia Lai
In this note, we extend our previous work on the inverse problem. Inverse problem is a fully nonlinear geometric PDE on compact Kähler manifolds. Given a proper geome…
On a class of fully nonlinear flow in Kähler geometry
Hao Fang, Mijia Lai, Xinan Ma
In this paper, we study a class of fully nonlinear metric flow on Kähler manifolds, which includes the J-flow as a special case. We provide a sufficient and necessary condition for…