## Publications

**Refereed Journal Articles**

Xavier Ramos Olivé, Shoo Seto, Guofang Wei, Qi S. Zhang.

*Zhong-Yang type*

*eigenvalue*

*estimate with integral curvature condition*, Mathematische Zeitschrift, December 2019.

Xavier Ramos Olivé.

*Neumann*

*Li-Yau gradient estimate under integral Ricci curvature bounds*, Proceedings of the American Mathematical Society,

**147**, No. 1, January 2019, Pages 411–426.

**Preprints**

Olaf Post, Xavier Ramos Olivé, Christian Rose. Quantitative Sobolev extensions and the Neumann heat kernel for integral Ricci curvature conditions, arXiv:2007.04120

**[math.DG]**.

## Research interests

I work on Geometric Analysis. I am interested in how local properties (like curvature) affect global properties (like the spectrum of the Laplacian). I use differential equations to understand these phenomena. More specifically, I am interested in heat kernel and eigenvalue estimates on manifolds with integral Ricci curvature bounds. Here is a copy of my research statement.

I received my PhD in Mathematics at the University of California, Riverside, under the supervision Qi S. Zhang.

I am also interested in Mathematical Physics, Differential Geometry, and their interplay. You can find here my CV.

I received my PhD in Mathematics at the University of California, Riverside, under the supervision Qi S. Zhang.

I am also interested in Mathematical Physics, Differential Geometry, and their interplay. You can find here my CV.