Event

Talk
Blow-up in the parabolic scalar curvature equation
Dr. Brian Smith
15 May 2007, 17:30 – 18:30

Consider a manifold foliated by hypersurfaces. Suppose that the intrinsic geometry of the hypersurfaces has been specified. We would like to obtain a manifold of prescribed scalar curvature in a non-conformal way by modifying the metric only in a direction transverse to the foliation. If the hypersurfaces are to have positive mean curvature, this gives rise to a nonlinear parabolic equation for the transversal component of the metric in which the foliating function plays the role of the time variable. It is easily seen by using the maximum principle that in many cases of physical interest the solution blows up. In this talk we consider the situation in which the blow-up corresponds to a horizon, and the stability of this phenomenon is addressed.

Related to:

• Brian Smith