Kai Xu

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math.DG2024

A topological gap theorem for the $I ¨ _{2}$ -systole of positive scalar curvature 3-manifolds

Kai Xu

Let $M$ be a closed orientable 3-manifold with scalar curvature greater than or equal to 1. If $M$ has nonvanishing second homotopy group, then it is known that the $I ¨ _{2}$ -systole…

math.DG2024

Dimension constraints in some problems involving intermediate curvature

Kai Xu

In arXiv:2207.08617 [math.DG] Brendle-Hirsch-Johne proved that $T^{m} \times S^{n - m}$ does not admit metrics with positive $m$ -intermediate curvature when $n \leq 7$ . Chu-Kwong-Lee sho…

math.DG2024

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…

A topological gap theorem for the I¨2​-systole of positive scalar curvature 3-manifolds

Dimension constraints in some problems involving intermediate curvature

Isoperimetry and the properness of weak inverse mean curvature flow

A topological gap theorem for the $I ¨ _{2}$ -systole of positive scalar curvature 3-manifolds