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.

**I am on the postdoc job market during Fall 2024.**

Here is my CV.

Contact me: kx35@math.duke.edu.

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

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

- Apr 2024: Geometric analysis seminar, Peking University / BICMR (online).
- Apr 2024: Geometry seminar, Michigan State University.
- Mar 2024: Geometric analysis and topology seminar, New York University / Courant Institute.
- Mar 2024: Geometry seminar, Chinese University of Hong Kong.
- Feb 2024: BIRS Workshop "Recent advances in comparison geometry", IASM Hangzhou, China.
- Nov 2023: Geometry and topology seminar, Duke University.
- Oct 2023: Geometric analysis seminar, University of Chicago.
- Oct 2023: Geometry seminar, Westlake University (online).
- Oct 2023: Geometry seminar, Stanford University.
- Jul 2023: CUHK-CUNY compactness and scalar curvature workshop (online).
- Oct 2022: Geometry seminar, North Carolina State University.

- 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