Jingbo Wan

• Columbia University

In this work, we consider the area non-increasing map between manifolds with positive curvature. By exploring the strong maximum principle along the graphical mean curvature flow, we show that an area non-increasing map between certain positively curved manifolds is either homotopy trivial, Riemannian submersion, local isometry or isometric immersi...

Kerr stability for small angular momentum has been proved in the series of works by Klainerman-Szeftel, Giorgi-Klainerman-Szeftel and Shen. Some of the most basic conclusions of the result, concerning various physical quantities on the future null infinity are derived in the work of Klainerman-Szeftel. Further important conclusions were later deriv...

We establish boundedness and polynomial decay results for the Teukolsky system in the exterior spacetime of very slowly rotating and strongly charged sub-extremal Kerr-Newman black holes, with a focus on axially symmetric solutions. The key step in achieving these results is deriving a physical-space Morawetz estimate for the associated generalized...

We prove the sharp interior gradient estimate for area decreasing graphical mean curvature flow in arbitrary codimension, which generalizes the result in \cite{CM}.

In this work, we consider the area non-increasing map between manifolds with positive curvature. By exploring the strong maximum principle along the graphical mean curvature flow, we show that an area non-increasing map between positively curved manifolds is either homotopy trivial , Riemannian submersion, local isometry or isometric immersion. Thi...

Consider a compact manifold N (with or without boundary) of dimension n . Positive m -intermediate curvature interpolates between positive Ricci curvature ( $$m = 1$$ m = 1 ) and positive scalar curvature ( $$m = n-1$$ m = n - 1 ), and it is obstructed on partial tori $$N^n = M^{n-m} \times \mathbb {T}^m$$ N n = M n - m × T m . Given Riemannian met...

Motivated by the recent work of Tsai-Tsui-Wang, we consider the rigidity of map between compact manifolds with positive curvature. We show that distance non-increasing map between complex projective spaces is either an isometry or homotopically trivial, which partially solves a question of Tsai-Tsui-Wang about weakly contracting maps. The rigidity...

Consider a compact manifold $N$ (with or without boundary) of dimension $n$. Positive $m$-intermediate curvature interpolates between positive Ricci curvature ($m = 1$) and positive scalar curvature ($m = n-1$), and it is obstructed on partial tori $N^n = M^{n-m} \times \mathbb{T}^m$. Given Riemannian metrics $g, \bar{g}$ on $(N, \partial N)$ with...

We study axisymmetric solutions to the wave equation on extremal Kerr backgrounds and obtain integrated local energy decay (or Morawetz estimates) through an analysis \textit{exclusively in physical-space}. Boundedness of the energy and Morawetz estimates for axisymmetric waves in extremal Kerr were first obtained by Aretakis through the constructi...

It is known from the literature that round spheres are the only closed homothetic self-similar solutions to the inverse mean curvature flow and parabolic curvature flows by degree − 1 -1 homogeneous functions of principal curvatures in the Euclidean space. In this article, we prove that the round sphere is rigid in a stronger sense: under some natu...

It has been known in that round spheres are the only closed homothetic self-similar solutions to the inverse mean curvature flow and many other curvature flows by degree -1 homogeneous functions of principle curvatures in the Euclidean space. In this article, we prove that the round sphere is rigid in much stronger sense, that under some natural co...