A compactness theorem for rotationally symmetric Riemannian manifolds with 
positive scalar curvature

Park, Jiewon; Tian, Wenchuan; Wang, Changliang

doi:10.4310/PAMQ.2018.v14.n3.a5

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

A compactness theorem for rotationally symmetric Riemannian manifolds with positive scalar curvature

MPS-Authors

/persons/resource/persons246347

Wang, Changliang
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://dx.doi.org/10.4310/PAMQ.2018.v14.n3.a5
(Publisher version)

https://doi.org/10.48550/arXiv.1812.03502
(Preprint)

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

There are no public fulltexts stored in PuRe

Supplementary Material (public)

There is no public supplementary material available

Citation

Park, J., Tian, W., & Wang, C. (2018). A compactness theorem for rotationally symmetric Riemannian manifolds with positive scalar curvature. Pure and Applied Mathematics Quarterly, 14(3-4), 529-561. doi:10.4310/PAMQ.2018.v14.n3.a5.

Cite as: https://hdl.handle.net/21.11116/0000-0009-F375-1

Abstract

Gromov and Sormani conjectured that sequences of compact Riemannian manifolds
with nonnegative scalar curvature and area of minimal surfaces bounded below
should have subsequences which converge in the intrinsic flat sense to limit
spaces which have nonnegative generalized scalar curvature and Euclidean
tangent cones almost everywhere. In this paper we prove this conjecture for
sequences of rotationally symmetric warped product manifolds. We show that the
limit spaces have $H^1$ warping function that has nonnegative scalar curvature
in a weak sense, and have Euclidean tangent cones almost everywhere.