Prescription de courbure des feuilles des laminations : retour sur un théorème de Candel
In the present paper, we revisit a famous theorem by Candel that we generalize by proving that given a compact lamination by hyperbolic surfaces, every negative function smooth inside the leaves and transversally continuous is the curvature function of a unique laminated metric in the corresponding...
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| Format: | article |
| Language: | French |
| Published: |
2021
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| Online Access: | https://hdl.handle.net/20.500.12008/35004 |
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| Summary: | In the present paper, we revisit a famous theorem by Candel that we generalize by proving that given a compact lamination by hyperbolic surfaces, every negative function smooth inside the leaves and transversally continuous is the curvature function of a unique laminated metric in the corresponding conformal class. We give an interpretation of this result as a continuity result about the solutions of some elliptic PDEs in the so called Cheeger–Gromov topology on the space of complete pointed riemannian manifolds. |
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