A renormalized Perelman-functional and a lower bound for the ADM-mass

Details A renormalized Perelman-functional and a lower bound for the ADM-mass A renormalized Perelman-functional and a lower bound for the ADM-mass

2011-01-06

arxiv.org/abs/1101.1226v2

J.Geom.Phys.61:2162-2167,2011

Mathematics

Differential Geometry

8 pages (v2: announced mass decreasing flow in dimension three; minor additional improvements)

Scientific paper

10.1016/j.geomphys.2011.06.016

In the first part of this short article, we define a renormalized F-functional for perturbations of non-compact steady Ricci solitons. This functional motivates a stability inequality which plays an important role in questions concerning the regularity of Ricci-flat spaces and the non-uniqueness of the Ricci flow with conical initial data. In the second part, we define a geometric invariant lambda_AF for asymptotically flat manifolds with nonnegative scalar curvature. This invariant gives a quantitative lower bound for the ADM-mass from general relativity, motivates a Ricci flow proof of the rigidity statement in the positive mass theorem, and eventually leads to the discovery of a mass decreasing flow in dimension three.

Affiliated with

Also associated with

No associations

Rating

A renormalized Perelman-functional and a lower bound for the ADM-mass 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 A renormalized Perelman-functional and a lower bound for the ADM-mass, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A renormalized Perelman-functional and a lower bound for the ADM-mass will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-399568