The barycenter method on singular spaces

• Autores: Peter A. Storm
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 82, Nº 1, 2007, págs. 133-173
• Idioma: inglés
• DOI: 10.4171/cmh/87
• Texto completo no disponible (Saber más ...)
• Resumen

  • Compact convex cores with totally geodesic boundary are proven to uniquely minimize volume over all hyperbolic 3-manifolds in the same homotopy class. This solves a conjecture in Kleinian groups concerning acylindrical 3-manifolds. Closed hyperbolic manifolds are proven to uniquely minimize volume over all compact hyperbolic cone-manifolds in the same homotopy class with cone angles =2p. Closed hyperbolic manifolds are proven to minimize volume over all compact Alexandrov spaces with curvature bounded below by -1 in the same homotopy class. A version of the Besson¿Courtois¿Gallot theorem is proven for n-manifolds with boundary. The proofs extend the techniques of Besson¿Courtois¿Gallot.