Park City Lectures on Eigenfunctions, Lecture 5: Lp norms of ...

Example: Irrational flat torus
Let (M, g) be a flat irrational torus R n /L where L ⊂ R n is a
co-compact lattice. In this case, the eigenfunctions are e i〈λ,x〉 with
λ ∈ L ∗ .
The multiplicities are 2 and it is easy to see that
L p (λ, g) = l p (λ, g) = 1.
How often do we find uniformly bounded eigenfunctions? Are there
any examples besides the flat torus? (In fact no! if you restrict
(M, g) to cases with integrable geodesic flow).