PDE seminar: α-Gauss Curvature flows with flat sides

2013-10-21 16:30 - 2013-10-21 17:30
Faculty of Science Building #3, Room 309
Lami Kim (Hokkaido University)
In this talk, we introduce α-Gauss Curvature flow
and for 1/2 < α ≤ 1, we show that there is smooth
solution if the initial data is smooth and strictly
convex and that there is a viscosity solution with
C1,1-estimate before the collapsing time if the initial
surface is only convex. Moreover, we prove that
there is a waiting time effect which means the flat
spot of the convex surface will persist for a while.
We also discuss the interface between the flat side
and the strictly convex side of the surface remains
smooth on 0 < t < T0 under certain necessary regularity
and non-degeneracy initial conditions, where
T0 is the vanishing time of the flat side. This talk is
based on joint work with K. Lee and E. Rhee.