We prove an uniform H\"older continuity of the resolvent of the Laplace-Beltrami operator on the real axis for a class of asymptotically Euclidean Riemannian manifolds. As an application we extend a result of Burq on the behaviour of the local energy of solutions to the wave equation.

MSC Classifications:

35B37, 35J15, 47F05 show english descriptions PDE in connection with control problems (See also 49J20, 49K20, 93C20)
Second-order elliptic equations
Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47) 35B37 - PDE in connection with control problems (See also 49J20, 49K20, 93C20)
35J15 - Second-order elliptic equations
47F05 - Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47)

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