Abstract
Suppose {(M, g(t)), 0 ≤ t < ∞} is a Kahler Ricci flow solution on a Fano surface. If |Rm| is not uniformly bounded along this flow, we can blowup at the maximal curvature points to obtain a limit complete Riemannian manifold X. We show that X must have certain topological and geometric properties. Using these properties, we are able to prove that |Rm| is uniformly bounded along every Kahler Ricci flow on toric Fano surface, whose initial metric has toric symmetry. In particular, such a Kahler Ricci flow must converge to a Kahler Ricci soliton metric. Therefore we give a new Ricci flow proof of the existence of Kahler Ricci soliton metrics on toric Fano surfaces.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
