Publications
Refereed Journal Articles
Xavier Ramos Olivé, Christian Rose, Lili Wang, Guofang Wei. Integral Ricci curvature and the mass gap of Dirichlet Laplacians on domains, Mathematische Nachrichten 296, 8 (2023), 3559–3578. https://doi.org/10.1002/mana.202100523
Olaf Post, Xavier Ramos Olivé, Christian Rose. Quantitative Sobolev extensions and the Neumann heat kernel for integral Ricci curvature conditions, Journal of Geometric Analysis 33, 70 (2023). https://doi.org/10.1007/s12220-022-01118-4
Xavier Ramos Olivé, Shoo Seto, Guofang Wei, Qi S. Zhang. Zhong-Yang type eigenvalue estimate with integral curvature condition, Mathematische Zeitschrift 296, 595-613 (2020). https://doi.org/10.1007/s00209-019-02448-w
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.
Research with Undergraduate Students
Connor C. Anderson, Xavier Ramos Olivé, Kamryn Spinelli. Manifolds with bounded integral curvature and no positive eigenvalue lower bounds, The PUMP Journal of Undergraduate Research, 4, 222–235 (2021).
Preprints
Shoo Seto, Xavier Ramos Olivé, Gradient estimates of a nonlinear parabolic equation under integral Bakry-Émery Ricci condition.
Xavier Ramos Olivé, Christian Rose, Lili Wang, Guofang Wei. Integral Ricci curvature and the mass gap of Dirichlet Laplacians on domains, Mathematische Nachrichten 296, 8 (2023), 3559–3578. https://doi.org/10.1002/mana.202100523
Olaf Post, Xavier Ramos Olivé, Christian Rose. Quantitative Sobolev extensions and the Neumann heat kernel for integral Ricci curvature conditions, Journal of Geometric Analysis 33, 70 (2023). https://doi.org/10.1007/s12220-022-01118-4
Xavier Ramos Olivé, Shoo Seto, Guofang Wei, Qi S. Zhang. Zhong-Yang type eigenvalue estimate with integral curvature condition, Mathematische Zeitschrift 296, 595-613 (2020). https://doi.org/10.1007/s00209-019-02448-w
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.
Research with Undergraduate Students
Connor C. Anderson, Xavier Ramos Olivé, Kamryn Spinelli. Manifolds with bounded integral curvature and no positive eigenvalue lower bounds, The PUMP Journal of Undergraduate Research, 4, 222–235 (2021).
Preprints
Shoo Seto, Xavier Ramos Olivé, Gradient estimates of a nonlinear parabolic equation under integral Bakry-Émery Ricci condition.
Research interests
I work on Geometric Analysis. I am interested in how local properties (like curvature) affect global properties (like the eigenvalues of the Laplacian). More specifically, I am interested in heat kernel and eigenvalue estimates on manifolds with integral Ricci curvature bounds. I am also interested in notions of Ricci curvature for discrete spaces, like graphs, and their applications to Data Science. Here is a copy of my research statement.
I received my PhD in Mathematics at the University of California, Riverside, under the supervision of 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 of Qi S. Zhang.
I am also interested in Mathematical Physics, Differential Geometry, and their interplay. You can find here my CV.
