کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1896323 | 1044425 | 2011 | 6 صفحه PDF | دانلود رایگان |
In the first part of this short article, we define a renormalized FF-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 λAFλAF 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.
► We define a renormalized FF-functional for non-compact manifolds.
► The FF-functional motivates a stability inequality for Ricci-flat spaces.
► We define a geometric invariant lambda for asymptotically flat manifolds.
► The lambda invariant gives a quantitative lower bound for the ADM-mass.
► We announce the discovery of a mass-decreasing flow in dimension three.
Journal: Journal of Geometry and Physics - Volume 61, Issue 11, November 2011, Pages 2162–2167