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Higher-order neck analysis of harmonic maps and its applications

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Abstract

In this paper, we prove some refined estimate in the neck region when a sequence of harmonic maps from surfaces blow up. The new estimate puts more restrictions to the bubble and the weak limit map than the touching required by the classical no-neck theorem. As an application, we prove an inequality about the nullity and index when blow-up occurs.

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Acknowledgements

The author would like to thank Professor Li Yuxiang for his comments.

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  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, China

    Hao Yin

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  1. Hao Yin
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Correspondence to Hao Yin.

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The research work is supported by NSFC 11471300, NSFC 11971451 and 2020YFA0713102.

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Yin, H. Higher-order neck analysis of harmonic maps and its applications. Ann Glob Anal Geom 62, 457–477 (2022). https://doi.org/10.1007/s10455-022-09858-w

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  • DOI: https://doi.org/10.1007/s10455-022-09858-w

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