Resumen de A Schläfli-Type Formula for Polytopes with Curved Faces and Its Application to the Kneser-Poulsen Conjecture

Balázs Csikós

• We prove a Schläfli-type formula for polytopes with curved faces lying in pseudo-Riemannian Einstein manifolds. This formula is applied to the Kneser-Poulsen conjecture claiming that the volume of the union of some balls cannot increase when the balls are rearranged in such a way that the distances between the centers decrease.