L-restriction Bounds for Eigenfunctions along Curves in the Quantum Completely Integrable Case

(1.1) ‖φj‖L∞ = O(λ n−1 2 j ). The example of the sphere shows that (1.1) is sharp. The corresponding sharp Lbounds are due to Sogge [So1, So2, So3]. Even thought this L-bound is far from generic [STZ], the only general improvements on (1.1) that we are aware of are due to Sogge and Zelditch [SZ] and more recently, Sogge, Toth and Zelditch [STZ, T4]. These authors obtain pointwise o(λ n−1 2 )-bounds under a certain non-recurrence condition for the geodesic flow on (M, g). The methods in [STZ] follow closely the earlier work of Safarov [S] and Safarov-Vassiliev [SV].