An infinite double bubble theorem

doi:10.4171/AIHPC/158

An infinite double bubble theorem

2026-03-01

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DOI：10.4171/AIHPC/158

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The classical double bubble theorem characterizes the minimizing partitions of R-n 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 R-n 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 & sup1;cjk degrees if for any Br.0/, it minimizes the interfacial energy Sigma(j= 8 under anatural growth assumption. We also obtain a closure theorem for locally minimizing (N,2) -clusters

Keyword:

double bubble

minimal surfaces

An infinite double bubble theorem

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