Introduction to and advances in the study of Willmore surfaces
Freitag, 11.4., 8:30, M103
The goal of the talk is two-fold. Firstly to introduce the notion of Willmore surfaces and recall the various physical contexts in which they arise. Secondly to show that the Willmore equation, a priori a 4th order problem, may be reduced to a system of two 2nd order equations. The algebraic structure of this system gives enough analytic suppleness to precisely study the behavior of a Willmore surface near a singular point (or equivalently to study the end of a non-compact Willmore surface) and obtain an identity describing the energy of the limit of a sequence of Willmore surfaces. Time permitting, I will also discuss other applications of the 2nd order system, in particular to the study of non-compact minimal surfaces in asymptotically flat manifolds. Most of what will be discussed is based on various joint-works with Tristan Rivière.
Roger Tagne Wafo
On the characteristic initial value problem for a class of nonlinear symmetric hyperbolic systems, including Einstein equations
Hn-Yamabe constants of Riemannian products with hyperbolic spaces
Conformal submanifold geometry
A submanifold N in a conformal-Riemannian manifold M can be considered to
be to be "totally geodesic" if: 1. It is totally geodesic for some
torsion-free conformal connection on M; 2. Every conformal geodesic of M,
strongly tangent to N, is contained in N; or
3. Every conformal geodesic in N is also a conformal geodesic in M.
These 3 notions coincide for M conformally flat, but turn out to be distinct
for curved ambient spaces M, and correspond to the vanishing of some
corresponding tensorial invariants of the embedding of N in M. Besides
these extrinsic curvature tensors, the embedding of N in M induces
two intrinsic structures on N: a Laplace structure (which is a
projective structure if N is a curve), and a Moebius structure if dim N>1.
Bernd Ammann, 9.4.2014 oder später