2,283 research outputs found
The isoperimetric inequality on asymptotically flat manifolds with nonnegative scalar curvature
In this note, we consider the isoperimetric inequality on an asymptotically
flat manifold with nonnegative scalar curvature, and improve it by using
Hawking mass. We also obtain a rigidity result when equality holds for the
classical isoperimetric inequality on an asymptotically flat manifold with
nonnegative scalar curvature.Comment: Final version, to appear International Mathematics Research Notices.
12 pages, no figure
Rigidity of Asymptotically Hyperboblic Manifolds
In this paper, we prove a rigidity theorem of asymptotically hyperbolic
manifolds only under the assumptions on curvature. Its proof is based on
analyzing asymptotic structures of such manifolds at infinity and a volume
comparison theorem.Comment: 16 page
Degenerations of Ricci-flat Calabi-Yau manifolds
This paper is a sequel to arXiv:1012.2940. We further investigate the
Gromov-Hausdorff convergence of Ricci-flat K\"{a}hler metrics under
degenerations of Calabi-Yau manifolds. We extend Theorem 1.1 in arXiv:1012.2940
by removing the condition on existence of crepant resolutions for Calabi-Yau
varieties.Comment: An error is correcte
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