Session S33 - Spectral Geometry

Tuesday, July 13, 15:00 ~ 15:20 UTC-3

Scarring of quasimodes on hyperbolic manifolds

Lior Silberman

The University of British Columbia, Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Let $M$ be a compact hyperbolic manifold. The entropy bounds of Anantharaman et al. restrict the possible invariant measures on $T^1 M$ that can be quantum limits of sequences of eigenfunctions. Weaker versions of the entropy bounds also apply to approximate eigenfuctions ("log-scale quasimodes"), so it is interesting to construct such approximate eigenfunctions which converges to singular measures.

Generalizing work of Brooks (hyperbolic surfaces) and Eswarathasan--Nonnenmacher (hyperbolic geodesics on Riemannian surfaces) we construct sequences of quasimodes on $M$ converging to totally geodesic submanifolds. A diagonal argument then realizes every invariant measure are a limit of quasimodes of fixed logarithmic width.

Joint work with Suresh Eswarathasan (Dalhousie University, Canada).

View abstract PDF