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Ming-Lun Liu

Publications and source records attributed to Ming-Lun Liu.

4 recordsLinked to original sources
arXiv2026

Energy identity for Intrinsic Stationary Biharmonic Mappings into Homogeneous Spaces in Supercritical Dimensions

In this paper, we consider energy identity for intrinsic stationary biharmonic maps into homogeneous spaces in supercritical dimensions, extending the corresponding result of Hornung-Moser [Anal. PDE. 2012] in critical dimension. The proof follows a similar strategy as that of Lin-Rivi\`ere [Duke Math. J. 2002]. A key ingredient is a conservation law for intrinsic biharmonic maps into homogeneous spaces, which allow us to derive higher regularity of the map.

math.AP↗
arXiv2025

Quantitative stratification and optimal regularity for harmonic almost complex structures

In a recent interesting work [15], W.Y. He established the important partial regularity theory and the almost optimal higher regularity theory for energy minimizing harmonic almost complex structures. Based on a new observation on the structure of equations, we give an easier new proof of the partial regularity theorem, and adapting the powerful quantitative stratification method of Naber-Valtorta [22], we further prove the rectifiability of singular stratum of energy minimizing harmonic almost complex structures. Based on this, we establish an optimal regularity theory, which improves the corresponding result of He.

math.AP↗
arXiv2024

$L^p$-regularity of a geometrically nonlinear system in supercritical dimensions

In a recent work, Gastel and Neff introduced an interesting system from a geometrically nonlinear flat cosserat micropolar model and established interior regularity in the critical dimension. Inspired by their work on this flat Cosserat model, in this article, we establish both interior regularity and sharp $L^p$ regularity for their system in supercritical dimensions.

math.AP↗