Nikolaos Roides; Adrian Spener
| 16:15 | Nikolaos Roidos (Hannover) | 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. |
| 17:45 | Adrian Spener (Ulm) | 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. |
