Calculus of Variations and Geometric Measure Theory

G. Di Matteo

Nondegeneracy of standard double bubbles

created by dimatteo on 01 Sep 2020


Published Paper

Inserted: 1 sep 2020

Journal: Proceedings of the American Mathematical Society
Volume: 147
Pages: 4379-4395
Year: 2019
Links: Journal Version


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.