A uniform contraction principle for bounded Apollonian embeddings
نویسندگان
چکیده
منابع مشابه
A Uniform Contraction Principle for Bounded Apollonian Embeddings
Let ̂ H = H ∪ {∞} denote the standard one-point completion of a real Hilbert space H. Given any non-trivial proper subset U ⊂ ̂ H one may define the so-called “Apollonian” metric dU on U . When U ⊂ V ⊂ ̂ H are nested proper subsets we show that their associated Apollonian metrics satisfy the following uniform contraction principle: Let Δ = diamV (U) ∈ [0,+∞] be the diameter of the smaller subsets ...
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ژورنال
عنوان ژورنال: Conformal Geometry and Dynamics of the American Mathematical Society
سال: 2011
ISSN: 1088-4173
DOI: 10.1090/s1088-4173-2011-00226-8