Welcome to my homepage. My name is Kai Xu.

I'm currently a graduate student at Duke University (expected graduation: 2025). My advisor is Prof. 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, the weak inverse mean curvature flow (both its analytic aspects and geometric applications), and Ricci curvature lower bounds in the spectral sense. I am also interested in geometric measure theory, and I am trying to employ some of its techniques in my works.

I am on the postdoc job market during Fall 2024.

Here is my CV.

Contact me: kx35@math.duke.edu.

Publications and preprints

  1. [arxiv] Inverse mean curvature flow with outer obstacle, preprint, 2024, submitted.
  2. [arxiv] joint with Gioacchino Antonelli, New spectral Bishop-Gromov and Bonnet-Myers theorems and applications to isoperimetry, preprint, 2024, submitted.
  3. [arxiv] joint with Demetre Kazaras and Antoine Song, Scalar curvature and volume entropy of hyperbolic 3-manifolds, preprint, 2023, submitted.
  4. [arxiv] joint with Demetre Kazaras, Drawstrings and flexibility in the Geroch conjecture, preprint, 2023, submitted.
  5. [arxiv] A topological gap theorem for the π2-systole of positive scalar curvature 3-manifolds, accepted by Duke Math. J. (2024).
  6. [arxiv][journal] Isoperimetry and the properness of weak inverse mean curvature flow, Calc. Var. Partial Differential Equations 63, 216 (2024).
  7. [arxiv] Dimension constraints in some problems involving intermediate curvature, accepted by Trans. Amer. Math. Soc. (2024).
  8. [arxiv] On closed surfaces with nonnegative curvature in the spectral sense, preprint, 2022, submitted.

Notes

Invited talks

Teaching