Weighted Sobolev inequalities and Ricci flat manifolds

Details Weighted Sobolev inequalities and Ricci flat manifolds Weighted Sobolev inequalities and Ricci flat manifolds

2006-02-07

arxiv.org/abs/math/0602136v2

Mathematics

Differential Geometry

Scientific paper

We prove a weighted Sobolev inequality and a Hardy inequality on manifolds
with nonnegative Ricci curvature satisfying an inverse doubling volume
condition. It enables us to obtain rigidity results for Ricci flat manifolds,
generalizing earlier work of Bando, Kasue and Nakajima.

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