Communications in Analysis and Geometry

Volume 29 (2021)

Number 5

Standard planar double bubbles are dynamically stable under surface diffusion flow

Pages: 1007 – 1060

DOI:  https://dx.doi.org/10.4310/CAG.2021.v29.n5.a1

Authors

Helmut Abels (Fakultät für Mathematik, Universität Regensburg, Germany)

Nasrin Arab (Uhldingen-Mühlhofen, Germany)

Harald Garcke (Fakultät für Mathematik, Universität Regensburg, Germany)

Abstract

Although standard planar double bubbles are stable in the sense that the second variation of the perimeter functional is non-negative for all area-preserving perturbations the question arises whether they are dynamically stable. By presenting connections between these two concepts of stability for double bubbles, we prove that standard planar double bubbles are dynamically stable under the surface diffusion flow via the generalized principle of linearized stability in parabolic Hölder spaces.

Received 21 June 2016

Accepted 28 November 2018

Published 1 December 2021