报告题目：Eigenvalue Estimate for the Rough Laplacian on 1-Forms and its Applications

报告人：黄腾副教授，中国科学技术大学

报告时间：2025年12月5日（周五）11:00

报告地点：腾讯会议183-965-748

报告摘要：In this talk, we establish a geometric lower bound for the first positive eigenvalue \lambda^{(1)}_{1}of the rough Laplacian acting on 1-forms for closed 2n-dimensional Riemannian manifolds with nonvanishing Euler characteristic. In contrast to the case of functions, such a Li-Yau-type estimate does not hold in general, as evidenced by existing counterexamples. Under assumptions including a lower bound on Ricci curvature, an upper bound on diameter, and an L^{2p}-norm bound on the Riemann curvature tensor, we prove that \lambda^{(1)}_{1} is bounded below by a positive constant depending on these parameters. As applications, we derive vanishing results for the Euler characteristic under certain Ricci curvature bounds and the presence of a nonzero Killing vector field, extending classical Bochner-type theorems. This is joint work with Weiwei Wang.

报告人简介：黄腾，现任中国科学技术大学数学科学学院副教授。主要研究方向为数学物理与微分几何。研究课题包括非负截面曲率流形、特殊和乐流形以及数学规范场论等。相关成果发表在Adv. Math.、Calc. Var. PDE、Int. Math. Res. Not.、Isr. J. Math、Math.Z.、Ann. Henri Poincaré等杂志上。

邀请人：任益斌