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.

中文翻译：

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标准平面双气泡在表面扩散流下是动态稳定的

尽管标准平面双气泡在周长泛函的第二个变化对于所有面积保持扰动都是非负的意义上是稳定的，但问题是它们是否是动态稳定的。通过提出这两个双气泡稳定性概念之间的联系，我们证明了标准平面双气泡在表面扩散流下通过抛物线霍尔德空间中线性化稳定性的广义原理是动态稳定的。