On spectral minimal partitions: the case of the sphere

Abstract

We consider spectral minimal partitions. Continuing work of the the present authors about problems for planar domains, [23], we focus on the sphere and obtain a sharp result for 3-partitions which is related to questions from harmonic analysis, in particular to a conjecture of Bishop.

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• Nodal sets of magnetic Schroedinger operators of Aharonov-Bohm type and energy minimizing partitions