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Jingbo Wan

Publications and source records attributed to Jingbo Wan.

23 records · Page 2Linked to original sources
arXiv2024

Boundedness and Decay for the Teukolsky System in Kerr-Newman Spacetime II: The Case $|a| \ll M$, $|Q| <M$ in Axial Symmetry

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 Regge-Wheeler system, without relying on spherical harmonic decomposition.

gr-qc↗
arXiv2024

Rigidity of area non-increasing maps

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 immersion. This implies that an area non-increasing self map of $\mathbb{CP}^n$, $n\ge 2$ is either homotopically trivial or is an isometry. This confirms a speculation of Tsai-Tsui-Wang. We also use Brendle's sphere Theorem and mean curvature flow coupled with Ricci flow to establish related results on manifolds with positive $1$-isotropic curvature.

math.DG↗
arXiv2023

Preserving positive intermediate curvature

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 positive $m$-intermediate curvature and $m$-positive difference $h_g - h_{\bar{g}}$ of second fundamental forms we show that there exists a smooth family of Riemannian metrics with positive $m$-intermediate curvature interpolating between $g$ and $\bar{g}$. Moreover, we apply this result to prove a non-existence result for partial torical bands with positive $m$-intermediate curvature and strictly $m$-convex boundaries.

math.DG↗
arXiv2020

Uniqueness Theorems of Self-Conformal Solutions to Inverse Curvature Flows

It has been known in that round spheres are the only closed homothetic self-similar solutions to the inverse mean curvature flow and parabolic 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 conditions such as star-shapedness, it is the only closed solution to the inverse mean curavture flow and the above-mentioned flows in the Euclidean space which evolves by diffeomorphisms generated by conformal Killing fields.

math.DG↗