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Abstract
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We study the relationship between
growth of eigenfunctions and their
concentration as measured by defect measures. In particular, we show that scarring in the
sense of concentration of defect measure on certain submanifolds is incompatible with
maximal
growth. In addition, we show that a defect measure which is too diffuse, such
as the Liouville measure, is also incompatible with maximal eigenfunction
growth.
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Keywords
eigenfunction, sup norms, defect measure
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Mathematical Subject Classification 2010
Primary: 35P20, 58J50
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Milestones
Received: 4 April 2017
Revised: 18 August 2017
Accepted: 16 October 2017
Published: 22 November 2017
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