ProV Logo
0
Volume comparison with respect to scalar...
Yuan, Wei...

Free

Volume comparison with respect to scalar curvature by Yuan, Wei ( Author )
Lemonjar Open Access
Australian National University
10-08-2023
In this article, we investigate the volume comparison with respect to scalar curvature. In particular, we show volume comparison holds for small geodesic balls of metrics near a V-static metric. For closed manifold, we prove the volume comparison for metrics near a strictly stable Einstein metric. As applications, we give a partial answer to a conjecture of Bray and recover a result of Besson, Courtois and Gallot, which partially confirms a conjecture of Schoen about closed hyperbolic manifold. Applying analogous techniques, we obtain a different proof of a local rigidity result due to Dai, Wang and Wei, which shows it admits no metric with positive scalar curvature near strictly stable Ricci-flat metrics.
-
Article
pdf
30.00 KB
English
-
MYR 0.01
-
http://arxiv.org/abs/1609.08849
Share this eBook