An integer degree for asymptotically conical self-expanders (Q6134275)

The authors establish the existence of an integer degree for the natural projection map from the space of parametrizations of asymptotically conical self-expanders to the space of parametrizations of the asymptotic cones when this map is proper. We recall that self-expanders are expected to model the behavior of a mean curvature flow as it emerges from a conical singularity. As an application they show that there is an open set in the space of cones in \({\mathbb R}^3\) for which each cone in the set has a strictly unstable self-expanding annuli asymptotic to it.