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Article Dans Une Revue Osaka Journal of Mathematics Année : 2014

Normal form of the metric for a class of Riemannian manifolds with ends

Résumé

In many problems of PDE involving the Laplace-Beltrami operator on manifolds with ends, it is often useful to introduce radial or geodesic normal coordinates near infinity. In this paper, we prove the existence of such coordinates for a general class of manifolds with ends, which contains asymptotically conical and hyperbolic manifolds. We study the decay rate to the metric at infinity associated to radial coordinates and also show that the latter metric is always conformally equivalent to the metric at infinity associated to the original coordinate system. We finally give several examples illustrating the sharpness of our results.

Dates et versions

hal-00988708 , version 1 (09-05-2014)

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Jean-Marc Bouclet. Normal form of the metric for a class of Riemannian manifolds with ends. Osaka Journal of Mathematics, 2014, 51 (4), pp.993-1015. ⟨hal-00988708⟩
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