Abstract.
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.
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Supported by the Hungarian National Science and Research Foundation OTKA T047102.
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Csikós, B. A Schläfli-Type Formula for Polytopes with Curved Faces and Its Application to the Kneser-Poulsen Conjecture. Mh Math 147, 273–292 (2006). https://doi.org/10.1007/s00605-005-0363-7
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DOI: https://doi.org/10.1007/s00605-005-0363-7