An Infinite Double Bubble Theorem

2024/01/16 by Bronsard, Lia, Novack, Michael · 2 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2401.08063

Abstract

The classical double bubble theorem characterizes the minimizing partitions of ℝⁿ into three chambers, two of which have prescribed finite volume. In this paper we prove a variant of the double bubble theorem in which two of the chambers have infinite volume. Such a configuration is an example of a (1,2)-cluster, or a partition of ℝⁿ into three chambers, two of which have infinite volume and only one of which has finite volume. A (1,2)-cluster is locally minimizing with respect to a family of weights \c_jk\ if for any B_r(0), it minimizes the interfacial energy ∑_j

Cited by

• Multi-Bubble Isoperimetric Problems
• On the non-uniqueness of locally minimizing clusters via singular cones

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