# MathSciDoc: An Archive for Mathematician ∫

#### Distinguished Paper Award in 2018

Ann. of Math. (2), 186, (2), 607-640, 2017.8
We show that $\lim_{t \to 0} e^{it\Delta}f(x) = f(x)$ almost everywhere for all $f \in H^s (\mathbb{R}^2)$ provided that $s>1/3$. This result is sharp up to the endpoint. The proof uses polynomial partitioning and decoupling.
restriction, Schrödinger equation, Schrödinger maximal function, polynomial partitioning, decoupling
@inproceedings{xiumin2017a,
title={A Sharp Schrödinger Maximal Estimate in R^2},
author={Xiumin Du, Larry Guth, and Xiaochun Li},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20181031043006873368171},
booktitle={Ann. of Math. (2)},
volume={186},
number={2},
pages={607-640},
year={2017},
}

Xiumin Du, Larry Guth, and Xiaochun Li. A Sharp Schrödinger Maximal Estimate in R^2. 2017. Vol. 186. In Ann. of Math. (2). pp.607-640. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20181031043006873368171.