Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature

Details Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature

2003-01-07

arxiv.org/abs/math/0301047v1

J. Differential Geometry, v. 62 (2002), p. 79-125.

Mathematics

Differential Geometry

35 pages

Scientific paper

In this paper, we study the boundary behaviors of compact manifolds with nonnegative scalar curvature and with nonempty boundary. Using a general version of Positive Mass Theorem of Schoen-Yau and Witten, we prove the following theorem: For any compact manifold with boundary and nonnegative scalar curvature, if it is spin and its boundary can be isometrically embedded into Euclidean space as a strictly convex hypersurface, then the integral of mean curvature of the boundary of the manifold cannot be greater than the integral of mean curvature of the embedded image as a hypersurface in Euclidean space. Moreover, equality holds if and only if the manifold is isometric with a domain in the Euclidean space. Conversely, under the assumption that the theorem is true, then one can prove the ADM mass of an asymptotically flat manifold is nonnegative, which is part of the Positive Mass Theorem.

Affiliated with

Also associated with

No associations

Rating

Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-722502