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Lower bounds for Cauchy data on curves in a negatively curved surface

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Abstract

We prove a uniform lower bound on Cauchy data on an arbitrary curve on a negatively curved surface using the Dyatlov-Jin(-Nonnenmacher) observability estimate on the global surface. In the process, we prove some further results about defect measures of restrictions of eigenfunctions to a hypersurface.

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Acknowledgements

This work was largely written during the period when both authors were research members at the Mathematical Sciences Research Institute. S. Z. would like to acknowledge support under NSF grant DMS-1810747. We would also like to thank the referee for a very careful reading which improved the exposition.

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Authors and Affiliations

  1. Department of Mathematics, University College, London, WC1E 6BT, UK

    Jeffrey Galkowski

  2. Department of Mathematics, Northwestern University, Evanston, IL, 60208-2370, USA

    Steve Zelditch

Authors
  1. Jeffrey Galkowski
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  2. Steve Zelditch
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Correspondence to Jeffrey Galkowski.

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Galkowski, J., Zelditch, S. Lower bounds for Cauchy data on curves in a negatively curved surface. Isr. J. Math. 244, 971–1000 (2021). https://doi.org/10.1007/s11856-021-2201-6

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  • DOI: https://doi.org/10.1007/s11856-021-2201-6

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