Some Classifications of Conformal Biharmonic and k-polyharmonic Maps

We give a complete classification of local and global conformal biharmonic maps between any two space forms by proving that a conformal map between two space forms is proper biharmonic if and only if the dimension is 4, the domain is flat, and it is a restriction of a Möbius transformation. We also...

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Veröffentlicht in:Frontiers of Mathematics 2023, Vol.18 (1), p.1-15
1. Verfasser: Ou, Ye-Lin
Format: Artikel
Sprache:eng
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Zusammenfassung:We give a complete classification of local and global conformal biharmonic maps between any two space forms by proving that a conformal map between two space forms is proper biharmonic if and only if the dimension is 4, the domain is flat, and it is a restriction of a Möbius transformation. We also show that proper k -polyharmonic conformal maps between Euclidean spaces exist if and only if the dimension is 2 k and they are precisely the restrictions of Möbius transformations. This provides infinitely many simple examples of proper k -polyharmonic maps with nice geometric structure.
ISSN:2731-8648
1673-3452
2731-8656
1673-3576
DOI:10.1007/s11464-021-0284-3