Spectrum of the drift Laplacian on Ricci expanders

主讲人：周德堂 巴西Fluminense联邦大学教授

时间：2025年6月28日10：00

地点：徐汇校区三号楼332室

举办单位：数理学院

主讲人介绍：周德堂，巴西 Fluminense联邦大学教授。 1991年博士毕业于山东大学。曾为山东大学教授，复旦大学、日本东北大学博士后， IMPA、 IHES、加州大学、 MIT等访问教授。研究成果发表在 J. Diff. Geom., Trans. Amer. Math. Soc., Math. Ann., Amer. J. Math., Crelle Journal等国际知名杂志上 。

内容介绍：We show that the spectrum is discrete when the potential function is proper, and we show that the hypothesis on the properness of the potential function cannot be removed. We conclude that the drift Laplacian has a discrete spectrum on Ricci expanders whose Ricci curvature is bounded below by a suitable constant. Further, we compute all the eigenvalues of the drift Laplacian on rigid expanders and rigid shrinkers. Lastly, we investigate the second eigenvalue of the drift Laplacian on rigid Ricci expanders whose Einstein factor is a closed hyperbolic Riemann surface. This is joint work with H. Leal and M. Vieira.