Standard Planar Double Bubbles are Stable under Surface Diffusion Flow

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 stable under the surface diffusion flow via the generalized principle of linearized stability in parabolic Hölder spaces.

48 pages, Section 6.1 and references for the introduction are added

References in corpus (1)

• On convergence of solutions to equilibria for quasilinear parabolic problems

Cited by in corpus (1)

• A structure-preserving finite element approximation of surface diffusion for curve networks and surface clusters