Kai Xu

activity

20002023

most citedHigher-Rank Tensor Non-Abelian Field Theory: Higher-Moment or Subdimensional Polynomial Global Symmetry, Algebraic Variety, Noether's Theorem, and Gauging

25 citations · 51 across the 12 of their papers we have counts for

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Showing 2023 · math.DGShow all

3 papers · 2 filters

math.DG2023

A topological gap theorem for the $π_{2}$ -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 $π_{2}$ -systole o…

math.DG2023

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…

math.DG2023

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…

A topological gap theorem for the π2​-systole of positive scalar curvature 3-manifolds

Isoperimetry and the properness of weak inverse mean curvature flow

Dimension constraints in some problems involving intermediate curvature

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