Nikolaos Roides; Adrian Spener
|Conic manifolds under the Yamabe flow
We consider the unnormalized Yamabe flow on manifolds with conical singularities. Under certain geometric assumption on the initial cross-section we show well posedness of the short time solution in the L^q-setting. Moreover, we give a picture of the deformation of the conical tips under the flow by providing an asymptotic expansion of the evolving metric close to the boundary in terms of the initial local geometry. Due to the blow up of the scalar curvature close to the singularities we use maximal L^q-regularity theory for conically degenerate operators.
|The elastic flow of curves in hyperbolic space (joint work with Anna
Dall'Acqua and Marius Müller, Ulm University)
In this talk we study the one-dimensional analogue of the Willmore flow
of closed curves in the hyperbolic plane. We show well-posedness and
long time existence of the flow, and prove sub-convergence under
additional length-penalisation. Furthermore, we discuss the necessity of
the assumption of penalisation.