Motivated by Giaquinta and Hildebrandt’s regularity result for harmonic mappings [M. Giaquinta and S. Hildebrandt, A priori estimates for harmonic mappings, J. Reine Angew. Math. 1982(336) (1982) 124–164, Theorems 3 and 4], we show a Cα,α2-regularity result of the harmonic flow between two Riemannian manifolds when the image is in a regular geodesic ball. The proof is based on De Giorgi–Moser’s iteration and Schauder estimate.

中文翻译：

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谐波热流的内部估计

受 Giaquinta 和 Hildebrandt 的调和映射规律性结果的启发 [M. Giaquinta 和 S. Hildebrandt，先验谐波映射的估计，J. Reine Angew。数学。 1982年(336) (1982) 124–164，定理 3 和 4]，我们展示了一个Cα,α2-当图像在规则测地线球中时，两个黎曼流形之间的谐波流的规则性结果。证明基于 De Giorgi-Moser 的迭代和 Schauder 估计。