Revista Matemática Iberoamericana


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Volume 32, Issue 3, 2016, pp. 995–999
DOI: 10.4171/RMI/905

Published online: 2016-10-03

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

Christopher D. Sogge[1] and Steve Zelditch[2]

(1) The Johns Hopkins University, Baltimore, USA
(2) Northwestern University, Evanston, USA

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’ $p$ so that all geodesics emanating from $p$ are smoothly closed.

Keywords: Eigenfunctions, $L^\infty$ bounds

Sogge Christopher, Zelditch Steve: Focal points and sup-norms of eigenfunctions II: the two-dimensional case. Rev. Mat. Iberoamericana 32 (2016), 995-999. doi: 10.4171/RMI/905