## Nondegeneracy of standard double bubbles

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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.## References

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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
- 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: https://doi.org/10.1090/proc/14551
- MathSciNet review: 4002550