25 citations · 51 across the 12 of their papers we have counts for
12 papers
A topological gap theorem for the -systole of positive scalar curvature 3-manifolds
Kai Xu
Let be a closed orientable 3-manifold with scalar curvature greater than or equal to 1. If has nonvanishing second homotopy group, then it is known that the -systole o…
Isoperimetry and the properness of weak inverse mean curvature flow
Kai Xu
We prove a new existence theorem for proper solutions of Huisken and Ilmanen's weak inverse mean curvature flow, assuming certain non-degeneracy conditions on the isoperimetric pro…
Dimension constraints in some problems involving intermediate curvature
Kai Xu
In arXiv:2207.08617 [math.DG] Brendle-Hirsch-Johne proved that does not admit metrics with positive -intermediate curvature when . Chu-Kwong-Lee sho…
On closed surfaces with nonnegative curvature in the spectral sense
Kai Xu
We study closed orientable surfaces satisfying the spectral condition , where is a positive constant and is the Gauss curvature. This condition natura…
The Cauchy problem of the Camassa-Holm equation in a weighted Sobolev space: Long-time and Painlevé asymptotics
Kai Xu, Yiling Yang, Engui Fan
Based on the -generalization of the Deift-Zhou steepest descent method, we extend the long-time and Painlevé asymptotics for the Camassa-Holm (CH) equation to th…
On Upper Bounds in Dimension Gaps of CFT's
Tristan C. Collins, Daniel Jafferis, Cumrun Vafa +2
We consider CFT's arising from branes probing singularities of internal manifolds. We focus on holographic models with internal space including arbtirary Sasaki-Einstein manifolds…