Sobolev spaces on Riemannian manifolds with bounded geometry: General coordinates and traces |
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Authors: | Nadine Große Cornelia Schneider |
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Affiliation: | 1. +49 2. 341 3. 9732132+49 4. 9732198;5. Mathematical Institute, University of Leipzig, , 04109 Leipzig, Germany;6. Applied Mathematics III, University of Erlangen–Nuremberg, , 91058 Erlangen, Germany |
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Abstract: | We study fractional Sobolev and Besov spaces on noncompact Riemannian manifolds with bounded geometry. Usually, these spaces are defined via geodesic normal coordinates which, depending on the problem at hand, may often not be the best choice. We consider a more general definition subject to different local coordinates and give sufficient conditions on the corresponding coordinates resulting in equivalent norms. Our main application is the computation of traces on submanifolds with the help of Fermi coordinates. Our results also hold for corresponding spaces defined on vector bundles of bounded geometry and, moreover, can be generalized to Triebel‐Lizorkin spaces on manifolds, improving [11]. |
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Keywords: | Sobolev spaces Riemannian manifolds bounded geometry Fermi coordinates traces vector bundles Besov spaces Triebel‐Lizorkin spaces 46E35 53C20 |
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