Welcome to my homepage. My name is Kai Xu.

I'm a Morrey Visiting Assistant Professor at UC Berkeley, mentored by Richard Bamler. I graduated from Duke University in 2025, under the supervision of Hubert Bray.

Research interests. I broadly enjoy problems in geometric analysis, calculus of variations, and metric geometry. My research is currently focused on the following topics: the geometry of scalar curvature (mainly in 3D), the weak inverse mean curvature flow, nonlinear potential theory (p-harmonic functions, where 1≤p≤∞), and Ricci curvature lower bounds in the spectral sense.

Here is my CV.

Contact me: kaixu@berkeley.edu.

Publications and preprints

  1. [arxiv] joint with Gioacchino Antonelli, Connected sum of manifolds with spectral Ricci lower bounds, preprint, 2025, submitted.
  2. [arxiv] joint with Otis Chodosh and Yi Lai, 3-Manifolds with positive scalar curvature and bounded geometry, preprint, 2025, submitted.
  3. [arxiv] joint with Demetre Kazaras, Codimension 2 drawstrings with scalar curvature lower bounds, preprint, 2025, submitted.
  4. [arxiv] joint with Gioacchino Antonelli and Marco Pozzetta, A sharp spectral splitting theorem, preprint, 2024, submitted.
  5. [arxiv] Inverse mean curvature flow with outer obstacle, preprint, 2024, submitted.
  6. [arxiv] joint with Gioacchino Antonelli, New spectral Bishop-Gromov and Bonnet-Myers theorems and applications to isoperimetry, preprint, 2024, submitted.
  7. [arxiv][journal] joint with Demetre Kazaras and Antoine Song, Scalar curvature and volume entropy of hyperbolic 3-manifolds, accepted by J. Eur. Math. Soc.
  8. [arxiv] joint with Demetre Kazaras, Drawstrings and flexibility in the Geroch conjecture, preprint, 2023, submitted.
  9. [arxiv][journal] A topological gap theorem for the π2-systole of positive scalar curvature 3-manifolds, Duke Math. J. 174(8), 1647-1664.
  10. [arxiv][journal] Isoperimetry and the properness of weak inverse mean curvature flow, Calc. Var. Partial Differential Equations 63, 216 (2024).
  11. [arxiv][journal] Dimension constraints in some problems involving intermediate curvature, Trans. Amer. Math. Soc. 378 (2025), 2091-2112.
  12. [arxiv] On closed surfaces with nonnegative curvature in the spectral sense, preprint, 2022, submitted.

Notes

Teaching

Invited talks