Welcome to my homepage. My name is Kai Xu.

I'm currently a graduate student at Duke University (starting Fall 2020). My advisor is Prof.
Hubert Bray.

I'm broadly interested in differential geometry, geometric analysis and metric geometry.
My research is currently concentrated on scalar curvature geometry, spectral curvature bounds,
and the inverse mean curvature flow.

Here is my CV.

Contact me: kx35@math.duke.edu.

- [arxiv]
**Inverse mean curvature flow with outer obstacle**, preprint, 2024. - [arxiv]
joint with Gioacchino Antonelli,
**New spectral Bishop-Gromov and Bonnet-Myers theorems and applications to isoperimetry**, preprint, 2024. - [arxiv]
joint with Demetre Kazaras
and Antoine Song,
**Scalar curvature and volume entropy of hyperbolic 3-manifolds**, preprint, 2023. - [arxiv]
joint with Demetre Kazaras,
**Drawstrings and flexibility in the Geroch conjecture**, preprint, 2023. - [arxiv]
**A topological gap theorem for the π2-systole of positive scalar curvature 3-manifolds**, preprint, 2023. - [arxiv]
**Isoperimetry and the properness of weak inverse mean curvature flow**, preprint, 2023. - [arxiv]
**Dimension Constraints in Some Problems Involving Intermediate Curvature**, preprint, 2023. - [arxiv]
**On closed surfaces with nonnegative curvature in the spectral sense**, preprint, 2022.

- [pdf]
**A note on the stable Bernstein theorem**, written with Gioacchino Antonelli.

- Spring 2024: Math 218D
- Fall 2023: Math 111L
- Spring 2023: Math 111L
- Fall 2022: Math 553, 555 (grading)
- Spring 2022: Math 411, 621 (grading)
- Fall 2021: Math 111L