Control of eigenfunctions on hyperbolic surfaces: an application of fractal uncertainty principle
Semyon Dyatlov1
1 Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 02139, USA
Journées équations aux dérivées partielles (2017), Talk no. 4, 14 p.

This expository article, written for the proceedings of the Journées EDP (Roscoff, June 2017), presents recent work joint with Jean Bourgain [BD16] and Long Jin [DJ17]. We in particular show that eigenfunctions of the Laplacian on hyperbolic surfaces are bounded from below in L 2 norm on each nonempty open set, by a constant depending on the set but not on the eigenvalue.

Published online:
DOI: 10.5802/jedp.654
Semyon Dyatlov 1

1 Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 02139, USA 
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Semyon Dyatlov. Control of eigenfunctions on hyperbolic surfaces: an application of fractal uncertainty principle. Journées équations aux dérivées partielles (2017), Talk no. 4, 14 p. doi : 10.5802/jedp.654. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.654/

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