Nondegeneracy of standard double bubbles

Di Matteo, Gianmichele

doi:10.1090/proc/14551

Nondegeneracy of standard double bubbles
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by Gianmichele Di Matteo PDF

Proc. Amer. Math. Soc. 147 (2019), 4379-4395 Request permission

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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