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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A blow-up formula for stationary quaternionic maps
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by Jiayu Li and Chaona Zhu
Proc. Amer. Math. Soc. 151 (2023), 4941-4948
DOI: https://doi.org/10.1090/proc/16476
Published electronically: June 16, 2023

Abstract:

Let $(M, J^\alpha , \alpha =1,2,3)$ and $(N, \mathcal {J}^\alpha , \alpha =1,2,3)$ be Hyperkähler manifolds. Suppose that $u_k$ is a sequence of stationary quaternionic maps and converges weakly to $u$ in $H^{1,2}(M,N)$, we derive a blow-up formula for $\lim _{k\to \infty }d(u_k^*\mathcal {J}^\alpha )$, for $\alpha =1,2,3$, in the weak sense. As a corollary, we show that the maps constructed by Chen-Li [Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 4 (2005), pp. 375–388] and by Foscolo [J. Differential Geom. 112 (2019), pp. 79–120] cannot be tangent maps (c.f Li and Tian [Internat. Math. Res. Notices 14 (1998), pp. 735–755], Theorem 3.1) of a stationary quaternionic map satisfing $d(u^*\mathcal {J}^\alpha )=0$.
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Bibliographic Information
  • Jiayu Li
  • Affiliation: School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, People’s Republic of China
  • MR Author ID: 274510
  • Email: jiayuli@ustc.edu.cn
  • Chaona Zhu
  • Affiliation: School of Mathematics and Statistics, Ningbo University, No. 818, Fenghua Road, Ningbo 315211, People’s Republic of China; and Dipartimento di Matematica dell’ Università degli studi di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Roma, Italia
  • MR Author ID: 1305298
  • Email: zcn1991@mail.ustc.edu.cn
  • Received by editor(s): December 31, 2022
  • Received by editor(s) in revised form: March 6, 2023
  • Published electronically: June 16, 2023
  • Additional Notes: The second author is the corresponding author
  • Communicated by: Jiaping Wang
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 4941-4948
  • MSC (2020): Primary 53C26, 53C43, 58E12, 58E20
  • DOI: https://doi.org/10.1090/proc/16476
  • MathSciNet review: 4634895