Weighted Sobolev Inequalities and Ricci Flat Manifolds

By V. Minerbe. 2006

60 citations recorded by the source corpus.

Abstract.In this paper, we prove a weighted Sobolev inequality and a Hardy inequality on manifolds with nonnegative Ricci curvature satisfying a reverse volume doubling condition. It enables us to obtain rigidity results for Ricci flat manifolds.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/3c20f5afb8325187bde240db60013cb495681041

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Hardy-Poincaré, Rellich and uncertainty principle inequalities on Riemannian manifolds (2011, unknown): “[7], [9], [14], [18], [4], [23], [17], [19], and the references therein.”
Asymptotically cylindrical Calabi-Yau manifolds (2012, background): “Our proof follows the strategy expounded in [16]; see also [18, 32] for closely related results and applications.”
Sharp uncertainty principles on Riemannian manifolds: the influence of curvature (2013, background): “Theorem 1.2 can be included into the best constant program initiated by Aubin [4], and studied by Ledoux [30], Cheeger and Colding [12], Druet, Hebey and Vaugon [16], do Carmo and Xia [15], Minerbe [32], Li and Wang [31], etc.”
On the 1/H-flow by p-Laplace approximation: New estimates via fake distances under Ricci lower bounds (2019, background): “The theorem, stated in [41, 55] for constant H , also holds for each H ≥ 0 non-increasing and is, in fact, a consequence of the concavity of the area of )Br as a function of the volume: s↦ vh ( V −1 h (s) ) is strictly concave on R+.”