数学科学学院学术报告

--- 分析、偏微分方程与动力系统讨论班(2024秋季第14讲)

题目: Refined $L^p$ restriction estimate for eigenfunctions on Riemannian surfaces

报告人: 高传伟 （首都师范大学）

时间：2025-01-02   10：00-11：00  (周四上午)  

地点: 沙河主楼E606

摘要: We refine the $L^p$ restriction estimates for Laplace eigenfunctions on a Riemannian surface, originally established by Burq, Gérard, and Tzvetkov. First, we establish estimates for the restriction of eigenfunctions to arbitrary Borel sets on the surface, following the approach of Eswarathasan and Pramanik. Our results bridge the $L^p(M)$ estimates of Sogge and the $L^p$ restriction bounds of Burq, Gérard, and Tzvetkov, and are sharp for all $p \geq 2$, modulo a $\lambda^\epsilon$-loss. Second, we derive sharp estimates for the restriction of eigenfunctions to tubular neighborhoods of a curve with non-vanishing geodesic curvature. This is based on a joint work with Changxing Miao and Yakun Xi.

报告人简介: 高传伟，研究的方向是调和分析及其在偏微分方程中的应用。主要关注与限制性猜想有关的问题，例如局部光滑估计猜想，平方函数不等式，解耦不等式，Kakeya猜想、特征函数估计等。已在Proc.Lond.Math.Soc,J.Funct.Anal.,Math.Z. Science China math等国际著名期刊发表多篇论文。

邀请人：朱政

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