Uniform estimates of the resolvent of the Laplace-Beltrami operator on infinite volume Riemannian manifolds. II. (English) Zbl 1021.58016

Cardoso, F.; Vodev, G.

Ann. Henri Poincaré 3, No. 4, 673-691 (2002).

Summary: We prove uniform weighted high frequency estimates for the resolvent of the Laplace-Beltrami operator on connected infinite volume Riemannian manifolds under some natural assumptions on the metric on the ends of the manifold.
This extends previous resutls by N. Burq [Am. J. Math. 124, No. 4, 677-735 (2002; Zbl 1013.35109)] and G. Vodev [Part I, Commun. Partial Differ. Equations 27, 1437-1465 (2002; Zbl 1015.58005)].

MSC:

58J26	Elliptic genera
53C20	Global Riemannian geometry, including pinching
58J05	Elliptic equations on manifolds, general theory

Keywords:

uniform estimates; resolvent; Laplace-Beltrami operator; infinite volume Riemannian manifolds

Citations:

Zbl 1013.35019; Zbl 1015.58005; Zbl 1013.35109