Rough metrics, the Kato square root problem, and the continuity of a flow tangent to the Ricci flow

Mardi 22 septembre 2015 14:00-15:00 - Lashi Bandara - Université de Göteborg

Résumé : The Kato square root problem, resolved in 2002 by Auscher, Hofmann, Lacey, McIntosh and Tchamitchian, was formulated in terms of a first-order framework by Axelsson, Keith and McIntosh in 2005. This has allowed for the resolution of this problem on Riemannian manifolds under natural geometric assumptions. Recently, we have defined a class of Riemannian-like metrics called rough metrics that capture geometric invariances of the problem. These metrics have recently been applied to understanding a geometric flow tangential to the Ricci flow for compact manifolds with geometric singularities. In particular, we will demonstrate how the continuity of solutions to this flow can be obtained via homogeneous Kato square root estimates on compact manifolds.

Lieu : bât. 425 - 113-115

Rough metrics, the Kato square root problem, and the continuity of a flow tangent to the Ricci flow  Version PDF