Tangent cut loci on surfaces

Alessio Figalli (1) , Ludovic Rifford (2) , Cédric Villani (3)

1 Department of Mathematics and Statistics [Texas Tech]
2 JAD - Laboratoire Jean Alexandre Dieudonné
3 ICJ - Institut Camille Jordan

Given a smooth compact Riemannian surface, we prove that if a suitable convexity assumption on the tangent focal cut loci is satisfied, then all injectivity domains are semiconvex.

Domaines: Géométrie différentielle [math.DG]; Géométrie métrique [math.MG]; Optimisation et contrôle [math.OC]

Alessio Figalli, Ludovic Rifford, Cédric Villani. Tangent cut loci on surfaces. Differential Geometry and its Applications, 2011, 29 (2), pp.154. ⟨hal-00923307⟩