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- W4300641528 abstract "Let H denote the standard one-point completion of a real Hilbert space. Given any non-trivial proper sub-set U of H one may define the so-called `Apollonian' metric d_U on U. When U subset V subset H are nested proper subsets we show that their associated Apollonian metrics satisfy the following uniform contraction principle: Let D=diam_V (U) in [0,+infty] be the diameter of the smaller subsets with respect to the large. Then for every x,y in U we have d_V(x,y) leq tanh (D/4) d_U(x,y). In dimension one, this contraction principle was established by Birkhoff for the Hilbert metric of finite segments on RP^1. In dimension two it was shown by Dubois for subsets of the Riemann sphere. It is new in the generality stated here." @default.
- W4300641528 created "2022-10-03" @default.
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- W4300641528 date "2011-02-21" @default.
- W4300641528 modified "2023-09-26" @default.
- W4300641528 title "A uniform contraction principle for bounded Apollonian embeddings" @default.
- W4300641528 doi "https://doi.org/10.48550/arxiv.1102.4212" @default.
- W4300641528 hasPublicationYear "2011" @default.
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