On the geometric dependence of Riemannian Sobolev best constants

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We concerns here with the continuity on the geometry of the second Riemannian L^p-Sobolev best constant B_0(p,g) associated to the AB program. Precisely, for 1 <= p <= 2, we prove that B_0(p,g) depends continuously on g in the C^2-topology. Moreover, this topology is sharp for p = 2. From this discussion, we deduce some existence and C^0-compactness results on extremal functions.
19 pages

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Differential Geometry, Analysis of PDEs, 32Q10, 53C21

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http://salesiana.dossiersoluciones.com/handle/123456789/166658

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0708.2376
 http://arxiv.org/abs/0708.2376

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arXiv