Lipschitz Retractions in Hadamard Spaces via Gradient Flow Semigroups
2016 ◽
Vol 59
(4)
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pp. 673-681
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AbstractLet X(n), for n ∊ ℕ, be the set of all subsets of a metric space (X, d) of cardinality at most n. The set X(n) equipped with the Hausdorff metric is called a finite subset space. In this paper we are concerned with the existence of Lipschitz retractions r: X(n)→ X(n − 1) for n ≥ 2. It is known that such retractions do not exist if X is the one-dimensional sphere. On the other hand, Kovalev has recently established their existence if X is a Hilbert space, and he also posed a question as to whether or not such Lipschitz retractions exist when X is a Hadamard space. In this paper we answer the question in the positive.
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2007 ◽
Vol 4
(4)
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pp. 451-482
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2018 ◽
Vol 20
(31)
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pp. 20417-20426
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Keyword(s):
2015 ◽
Vol 93
(1)
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pp. 146-151
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Keyword(s):
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2013 ◽
Vol Vol. 15 no. 2
(Automata, Logic and Semantics)
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