Weighted floating bodies and polytopal approximation

Besau, Florian; Ludwig, Monika; Werner, Elisabeth

doi:10.1090/tran/7233

Weighted floating bodies and polytopal approximation

Authors: Florian Besau, Monika Ludwig and Elisabeth M. Werner
Journal: Trans. Amer. Math. Soc. 370 (2018), 7129-7148
MSC (2010): Primary 52A38; Secondary 52A27, 52A55, 53C60, 60D05.
DOI: https://doi.org/10.1090/tran/7233
Published electronically: April 4, 2018
MathSciNet review: 3841844
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Abstract: Asymptotic results for weighted floating bodies are established and used to obtain new proofs for the existence of floating areas on the sphere and in hyperbolic space and to establish the existence of floating areas in Hilbert geometries. Results on weighted best and random approximation and the new approach to floating areas are combined to derive new asymptotic approximation results on the sphere, in hyperbolic space, and in Hilbert geometries.

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