| Résume | I will present some results on the local behavior of geodesics on singular spaces and an families of smooth spaces degenerating to a singular space, where in both cases the singularity is isolated and cuspidal. Some surprising concentration phenomena occur for non-circular cross-section, which are also illustrated numerically. The talk is based on joint work with Vincent Grandjean and Jørgen Lye, and closely related to ongoing joint work with André Belotto, Antje Beyer and María Vega. The methods involve blow-ups to resolve the geodesic vector field combined with a detailed analysis of the suitably rescaled geodesic flow using the invariant manifold theorem. |
