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arXiv:1609.08849 [math.DG]AbstractReferencesReviewsResources

Volume comparison with respect to scalar curvature

Wei Yuan

Published 2016-09-28Version 1

In this article, we investigate the volume comparison with respect to scalar curvature. In particular, we show volume comparison hold for small geodesic balls of metrics near $V$-static metrics. As for global results, we give volume comparison for metrics near Einstein metrics with certain restrictions. As an application, we recover a volume comparison result of compact hyperbolic manifolds due to Besson-Courtois-Gallot, which provides a partial answer to a conjecture of Schoen on volume of hyperbolic manifolds.

Comments: 25 pages
Categories: math.DG
Subjects: 53C20, 58J37, 53C23, 53C24
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