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 norm on each nonempty open set, by a constant depending on the set but not on the eigenvalue.
@article{JEDP_2017____A4_0, author = {Dyatlov, Semyon}, title = {Control of eigenfunctions on hyperbolic surfaces: an application of fractal uncertainty principle}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, note = {talk:4}, pages = {1--14}, publisher = {Groupement de recherche 2434 du CNRS}, year = {2017}, doi = {10.5802/jedp.654}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jedp.654/} }
TY - JOUR AU - Dyatlov, Semyon TI - Control of eigenfunctions on hyperbolic surfaces: an application of fractal uncertainty principle JO - Journées équations aux dérivées partielles N1 - talk:4 PY - 2017 SP - 1 EP - 14 PB - Groupement de recherche 2434 du CNRS UR - http://archive.numdam.org/articles/10.5802/jedp.654/ DO - 10.5802/jedp.654 LA - en ID - JEDP_2017____A4_0 ER -
%0 Journal Article %A Dyatlov, Semyon %T Control of eigenfunctions on hyperbolic surfaces: an application of fractal uncertainty principle %J Journées équations aux dérivées partielles %Z talk:4 %D 2017 %P 1-14 %I Groupement de recherche 2434 du CNRS %U http://archive.numdam.org/articles/10.5802/jedp.654/ %R 10.5802/jedp.654 %G en %F JEDP_2017____A4_0
Dyatlov, Semyon. Control of eigenfunctions on hyperbolic surfaces: an application of fractal uncertainty principle. Journées équations aux dérivées partielles (2017), Exposé no. 4, 14 p. doi : 10.5802/jedp.654. http://archive.numdam.org/articles/10.5802/jedp.654/
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