Sharp Estimates for the Size of Balls in the Complement of a Hypersurface

In this paper, we make estimates for the radius of balls contained in some component of the complementary of a complete hypersurface into a space form, generalizing and improving analogous radius estimates for embedded compact hypersurfaces obtained by Blaschke, Koutroufiotis and the authors. The results are obtained using an algebraic lemma and a tangency principle related with the length of the second fundamental form. The algebraic lemma also is used to improve a result for graphs due to Hasanis–Vlachos. The first author dedicates this work to his parents José (in memoriam) and Herondina