Optimal Higher Regularity for Biharmonic Maps Via Quantitative Stratification

Abstract

This note is devoted to refining the almost optimal regularity results of Breiner and Lamm on minimizing and stationary biharmonic maps via the powerful quantitative stratification method initiated by Cheeger and Naber and significantly developed by Naber and Valtorta for harmonic maps. In particular, we obtain an optimal regularity result for minimizing biharmonic maps.

Keywords

Biharmonic maps / Regularity theory / Quantitative stratification / Quantitative symmetry / Singular set / 53C43 / 35J48

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Funding

National Natural Science Foundation of China(12271296)

RIGHTS & PERMISSIONS

Peking University