Geometry and Topology Seminar: Flowing to non-round Weingarten spheres.
18 February 2016 13:00 in CM221.
We study when a C^2 - smooth function K on the upper half plane occurs as the relation on the curvatures of a closed convex classical surface S. If K gives rise to a (nonlinear) elliptic relation at the umbilic points, then S is known to be a round sphere (Hopf). We prove that there exist *non-round* surfaces S in case the relation K is non-degenerate hyperbolic at the umbilics. The proof is by (nonlinear) curvature flow with speed K, which is shown to converge by establishing certain a-priori estimates.