Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


A blow-up formula for stationary quaternionic maps
HTML articles powered by AMS MathViewer

by Jiayu Li and Chaona Zhu
Proc. Amer. Math. Soc. 151 (2023), 4941-4948
Published electronically: June 16, 2023


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 $d(u^*\mathcal {J}^\alpha )=0$.
Similar Articles
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:
  • 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:
  • 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:
  • MathSciNet review: 4634895