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

• Autores: Balázs Csikós
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 147, Nº 4, 2006, págs. 273-292
• Idioma: inglés
• DOI: 10.1007/s00605-005-0363-7
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• Resumen

  • 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.