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Nondegeneracy of standard double bubbles


Author: Gianmichele Di Matteo
Journal: Proc. Amer. Math. Soc. 147 (2019), 4379-4395
MSC (2010): Primary 34C10, 53A10, 53C24, 53A24, 35J57
DOI: https://doi.org/10.1090/proc/14551
Published electronically: June 14, 2019
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Abstract: 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: g.dimatteo@qmul.ac.uk

DOI: https://doi.org/10.1090/proc/14551
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
Article copyright: © Copyright 2019 American Mathematical Society