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arXiv · 1002.0756

An alternative proof of a rigidity theorem for the sharp Sobolev constant

Stefano Pigola·Giona Veronelli
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Abstract

We provide a somewhat geometric proof of a rigidity theorem by M. Ledoux and C. Xia concerning complete manifolds with non-negative Ricci curvature supporting an Euclidean-type Sobolev inequality with (almost) best Sobolev constant. Using the same technique we also generalize Ledoux-Xia result to complete manifolds with asymptotically non-negative curvature.

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Stefano Pigola, Giona Veronelli. 2010-02-22. An alternative proof of a rigidity theorem for the sharp Sobolev constant. https://arxiv.org/abs/1002.0756

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