B.A., University of California, Santa Cruz
M.A., University of California, Santa Cruz
Ph.D., University of California, Santa Cruz
Differential Geometry, Geometric Analysis, Conformal Geometry and Mathematical Relativity
My research is in the fields of differential geometry and geometric analysis. I am particularly interested in the influence of curvature on global shape and the relationship between partial differential equations on manifolds and geometric problems. My recent research focuses on the application of analytic methods to asymptotically flat and asymptotically hyperbolic manifolds, which are significant in the mathematical theories of classic and quantum relativity. In the context of conformal geometry, my research in the asymptotically hyperbolic setting aims to strengthen the relation between the geometry and topology of certain conformally compact spaces and the geometry of their conformal infinities.
- Vincent Bonini, Conor Carroll, Uyen Dinh, Sydney Dye, Joshua Frederick, Erin Pearse, Condensed Ricci Curvature of Complete and Strongly Regular Graphs. Involve 13 (2020) no. 4, 559-576. https://doi.org/10.2140/involve.2020.13.559
- Vincent Bonini, Shiguang Ma, Jie Qing, Hypersurfaces with Nonnegative Ricci Curvature in Hyperbolic Space. J. Calc. Var. (2019) 58:36. https://doi.org/10.1007/s00526-018-1471-2
- Vincent Bonini, Shiguang Ma, Jie Qing, On Nonnegatively Curved Hypersurfaces in Hyperbolic Space. Math. Ann. 372 (2018) 1103-1120. https://doi.org/10.1007/s00208-018-1694-8
- Vincent Bonini, Jie Qing, Jingyong Zhu,Weakly Horospherically Convex Hypersurfaces in Hyperbolic Space. Annals of Global Analysis and Geometry. 52 (2017) no. 2, 201-212.
- Vincent Bonini, José M. Espinar, Jie Qing,Hypersurfaces in Hyperbolic Space with Horospherical Support Function, Advances in Mathematics, 280 (2015) 506-548.
- Vincent Bonini, José M. Espinar, Jie Qing, Correspondences of Hypersurfaces in Hyperbolic Poincaré Manifolds and Conformally Invariant PDEs. Proc. Amer. Math. Soc., 138 (2010) no.11, 4109-4117.
- Vincent Bonini, Jie Qing, A Positive Mass Theorem on Asymptotically Hyperbolic Manifolds with Corners Along a Hypersurface. Annales Henri Poincaré, 9 (2008) 347-372.
- Vincent Bonini, Pengzi Miao, Jie Qing, Ricci Curvature Rigidity for Weakly Asymptotically Hyperbolic Manifolds. Communications in Analysis and Geometry, 14 (2006) no. 3, 603-612.
- Vincent Bonini, Shiguang Ma, Jie Qing,On Convex Hypersurfaces in Hyperbolic Space. Surveys in Geometric Analysis 2017, Science Press, Beijing, 1-22.