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Bounding the number of nodal domains of eigenfunctions without singular points on the square

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Abstract

We prove Polterovich’s conjecture concerning the growth of the number of nodal domains for eigenfunctions on a unit square domain, under the assumption that the eigenfunctions do not have any singular points.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, College Station, TX, 77840, USA

    Junehyuk Jung

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  1. Junehyuk Jung
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Correspondence to Junehyuk Jung.

Additional information

We would like to thank Jean Bourgain for introducing the problem, and encouragement. We appreciate Stefan Steinerberger, Van Vu, Igor Wigman, Steve Zelditch, and Joon-Hyeok Yim for many helpful discussions. We also thank Bernard Helf-fer and the anonymous referee for detailed comments on the earlier version of the manuscript.

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Jung, J. Bounding the number of nodal domains of eigenfunctions without singular points on the square. Isr. J. Math. 238, 1–11 (2020). https://doi.org/10.1007/s11856-020-2021-0

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  • DOI: https://doi.org/10.1007/s11856-020-2021-0

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