Boundedness of Laplacian eigenfunctions on manifolds of infinite volume
Leonardo Bonorino, Patrícia Kruse Klaser, Miriam Telichevesky · Communications in Analysis and Geometry · 2016
In a Hadamard manifold M , it is proved that if u is a λeigenfunction of the Laplacian that belongs to L p (M ) for some p ≥ 2, then u is bounded and u L ∞ ≤ C u L p , where C depends only on p, λ and the dimension of M .This result is obtained in the more general context of a Riemannian manifold endowed with an isoperimetric function H satisfying some integrability condition.In this case, the constant C depends on p, λ and H.