Optimal higher regularity for biharmonic maps via quantitative stratification
Analysis of PDEs
2025-05-13 v1 Differential Geometry
Abstract
This little note is devoted to refining the almost optimal regularity results of Breiner and Lamm \cite{Breiner-Lamm-2015} on minimizing and stationary biharmonic maps via the powerful quantitative stratification method introduced by Cheeger and Naber \cite{Cheeger-Naber-2013} and further developed by Naber and Valtorta \cite{Naber-V-2017,Naber-V-2018} for harmonic maps. In particular, we obtain an optimal regularity results for minimizing biharmonic maps.
Keywords
Cite
@article{arxiv.2401.11177,
title = {Optimal higher regularity for biharmonic maps via quantitative stratification},
author = {Chang-Yu Guo and Gui-Chun Jiang and Chang-Lin Xiang and Gao-Feng Zheng},
journal= {arXiv preprint arXiv:2401.11177},
year = {2025}
}