Short-time existence for the second order renormalization group flow in general dimensions

Christine Guenther; James Isenberg; Karsten Gimre

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Short-time existence for the second order renormalization group flow in general dimensions

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arxiv 1401.1454 v1 pith:TFWMTAHS submitted 2014-01-07 math.DG

Short-time existence for the second order renormalization group flow in general dimensions

Karsten Gimre , Christine Guenther , James Isenberg This is my paper

classification math.DG

keywords dimensionsexistenceflowgeneralgroupinitialorderrenormalization

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We prove local existence for the second order Renormalization Group flow initial value problem on closed Riemannian manifolds $(M,g)$ in general dimensions, for initial metrics whose sectional curvatures $K_P$ satisfy the condition $1+\alpha K_P > 0$, at all points $p \in M$ and planes $P \subset T_p M$. This extends results previously proven for two and three dimensions.

Short-time existence for the second order renormalization group flow in general dimensions

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