A review on large k minimal spectral k-partitions and Pleijel's Theorem

Bernard Helffer, Thomas Hoffmann-Ostenhof

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

Abstract

In this survey, we review the properties of minimal spectral k-partitions in the two-dimensional case and revisit their connections with Pleijel's Theorem. We focus on the large k problem (and the hexagonal conjecture) in connection with two recent preprints by J. Bourgain and S. Steinerberger on the Pleijel Theorem. This leads us also to discuss some conjecture by I. Polterovich, in relation with square tilings. We also establish a Pleijel Theorem for Aharonov-Bohm Hamiltonians and deduce from it, via the magnetic characterization of the minimal partitions, some lower bound for the number of critical points of a minimal partition.
OriginalspracheEnglisch
Seiten (von - bis)39-58
FachzeitschriftContemporary Mathematics (CONM)
Jahrgang640
PublikationsstatusVeröffentlicht - 2015

ÖFOS 2012

  • 101002 Analysis

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