中科院数学与系统科学研究院
数学研究所
学术报告
调和分析和偏微分方程研讨班
报告人：金龙 （清华大学）
题 目：Control of eigenfunctions on surfaces of negative curvature
时 间：2022.06.28（星期二）17:00-18:00
地 点：腾讯会议：451-729-309
摘 要：In this talk, we present a uniform lower bound for the mass in any fixed nonempty open set of normalized Laplacian eigenfunctions on negatively curved surfaces, independent of eigenvalues. The result extends previous joint work with Semyon Dyatlov on surfaces with constant negative curvature. The proof relies on microlocal analysis, chaotic behavior of the geodesic flow and a new ingredient from harmonic analysis called Fractal Uncertainty Principle by Jean Bourgain and Semyon Dyatlov. Further applications include control for Schr\"{o}dinger equation and exponential decay of energy for damped waves. This is based on joint work with Semyon Dyatlov and St\'{e}phane Nonnenmacher.
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