The 2-dimensional Calabi flow
Journal
Nagoya Mathematical Journal
Journal Volume
181
Pages
63-73
Date Issued
2006
Author(s)
Abstract
In this paper, the authors consider the 3-dimensional local Calabi flow on noncompact 3-manifolds with a complete metric of nonpositive scalar curvature and negative somewhere. Then long-time existence and asymptotic convergence of a subsequence of solutions of the flow are claimed. For its applications, it is proved that every noncompact 3-manifold admits a complete extremal metric. In particular, there exists a complete metric on a noncompact 3-manifold, a counterexample to the Yamabe problem, which is conformal to a complete extremal metric of non-constant scalar curvature.
SDGs
Type
journal article