We provide sharp lower bounds for the simplicial volume of compact 3-manifolds in terms of the simplicial volume of their boundaries. As an application we show how to compute the simplicial volume of a handlebody and the product of a surface with the interval. Moreover, if there is enough time, we will give a complete characterization of hyperbolic n-manifolds (for n bigger or equal to 4) with geodesic boundary whose simplicial volume is close to the ratio between Riemannian volume and the volume of an ideal and regular simplex in the hyperbolic space. This is joint work with M. Bucher and R. Frigerio.

*Cristina Pagliantini, University of Regensburg*