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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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Nondegeneracy of standard double bubbles
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by Gianmichele Di Matteo PDF
Proc. Amer. Math. Soc. 147 (2019), 4379-4395 Request permission


In this paper we prove that all Jacobi fields of a standard double bubble in $\mathbb {R}^{m+1}$ are generated by infinitesimal translations and rotations. This implies that the degeneracy of the area functional on double bubbles is only generated by global isometries, with dimension $2m+1$. The proof relies on a Fourier expansion of the normal components of the Jacobi fields and on an accurate analysis of some ordinary differential equations.
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Additional Information
  • Gianmichele Di Matteo
  • Affiliation: Department of Mathematics, Queen Mary University of London, London E1 4NS, United Kingdom
  • Email:
  • Received by editor(s): December 6, 2018
  • Received by editor(s) in revised form: January 11, 2019, and January 21, 2019
  • Published electronically: June 14, 2019
  • Communicated by: Jia-Ping Wang
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4379-4395
  • MSC (2010): Primary 34C10, 53A10, 53C24, 53A24, 35J57
  • DOI:
  • MathSciNet review: 4002550