JournalsrmiVol. 32, No. 3pp. 995–999

Focal points and sup-norms of eigenfunctions II: the two-dimensional case

  • Christopher D. Sogge

    The Johns Hopkins University, Baltimore, USA
  • Steve Zelditch

    Northwestern University, Evanston, USA
Focal points and sup-norms of eigenfunctions II: the two-dimensional case cover
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Abstract

We use a purely dynamical argument on circle maps to improve a result in our accompanying article, [5], on real analytic surfaces possessing eigenfunctions that achieve maximal sup norm bounds. The improved result is that there exists a ‘pole’ pp so that all geodesics emanating from pp are smoothly closed.

Cite this article

Christopher D. Sogge, Steve Zelditch, Focal points and sup-norms of eigenfunctions II: the two-dimensional case. Rev. Mat. Iberoam. 32 (2016), no. 3, pp. 995–999

DOI 10.4171/RMI/905