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A New Conformal Heat Flow of Harmonic Maps

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Abstract

We introduce and study a conformal heat flow of harmonic maps defined by an evolution equation for a pair consisting of a map and a conformal factor of metric on the two-dimensional domain. This flow is designed to postpone finite time singularity but does not get rid of possibility of bubble forming. We show that Struwe type global weak solution exists, which is smooth except at most finitely many points.

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Acknowledgements

The author would like to thanks Armin Schikorra and Thomas Parker for valuable comments and advice. The author also thank to the referee for his careful reading and valuable suggestions.

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  1. Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA, 152660, USA

    Woongbae Park

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Park, W. A New Conformal Heat Flow of Harmonic Maps. J Geom Anal 33, 376 (2023). https://doi.org/10.1007/s12220-023-01432-5

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