Welcome to my homepage. My name is Kai Xu.

I'm a postdoc member at IAS Peinceton (starting Sep 2026), mentored by Aaron Naber. I was previously a postdoc 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), 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] Infinity-harmonic functions and inverse mean curvature flow clusters, preprint, 2026.
  2. [arxiv] joint with Luca Benatti, Luciano Mari, Marco Rigoli and Alberto G. Setti, Proper solutions of the 1/H-flow and the Green kernel of the p-Laplacian, preprint, 2025.
  3. [arxiv][journal] joint with Gioacchino Antonelli, Connected sum of manifolds with spectral Ricci lower bounds, Proc. Amer. Math. Soc. 154 (2026), no. 6, 2635–2647.
  4. [arxiv][journal] joint with Otis Chodosh and Yi Lai, 3-Manifolds with positive scalar curvature and bounded geometry, Comm. Pure Appl. Math. 79 (2026), no. 5, 1299–1314.
  5. [arxiv] joint with Demetre Kazaras, Codimension 2 drawstrings with scalar curvature lower bounds, preprint, 2025, submitted.
  6. [arxiv] joint with Gioacchino Antonelli and Marco Pozzetta, A sharp spectral splitting theorem, preprint, 2024, submitted.
  7. [arxiv] Inverse mean curvature flow with outer obstacle, preprint, 2024, Geom. Topol., to appear.
  8. [arxiv] joint with Gioacchino Antonelli, New spectral Bishop-Gromov and Bonnet-Myers theorems and applications to isoperimetry, preprint, 2024, J. Eur. Math. Soc., to appear.
  9. [arxiv][journal] joint with Demetre Kazaras and Antoine Song, Scalar curvature and volume entropy of hyperbolic 3-manifolds, J. Eur. Math. Soc., to appear.
  10. [arxiv] joint with Demetre Kazaras, Drawstrings and flexibility in the Geroch conjecture, preprint, 2023, J. Differential Geom., to appear.
  11. [arxiv][journal] A topological gap theorem for the π2-systole of positive scalar curvature 3-manifolds, Duke Math. J. 174(8), 1647-1664.
  12. [arxiv][journal] Isoperimetry and the properness of weak inverse mean curvature flow, Calc. Var. Partial Differential Equations 63, 216 (2024).
  13. [arxiv][journal] Dimension constraints in some problems involving intermediate curvature, Trans. Amer. Math. Soc. 378 (2025), 2091-2112.
  14. [arxiv] On closed surfaces with nonnegative curvature in the spectral sense, preprint, 2022, submitted.

Notes

Teaching

Invited talks