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On the gradient set of Lipschitz maps
 J. Rein. Ang. Math
"... Abstract. We prove that the essential range of the gradient of planar Lipschitz maps has a connected rankone convex hull. As a corollary, in combination with the results in [7] we obtain a complete characterization of incompatible sets of gradients for planar maps in terms of rankone convexity. 1. ..."
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Abstract. We prove that the essential range of the gradient of planar Lipschitz maps has a connected rankone convex hull. As a corollary, in combination with the results in [7] we obtain a complete characterization of incompatible sets of gradients for planar maps in terms of rankone convexity. 1.
ADJOINTS OF LIPSCHITZ MAPPINGS
"... Abstract. The aim of this paper is to show that the Lipschitz adjoint of a Lipschitz mapping F, defined by I. Sawashima, Lecture Notes Ec. Math. Syst., Vol. 419, Springer Verlag, Berlin 1975, pp. 247259, corresponds in a canonical way to the adjoint of a linear operator associated to F. 1. ..."
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Abstract. The aim of this paper is to show that the Lipschitz adjoint of a Lipschitz mapping F, defined by I. Sawashima, Lecture Notes Ec. Math. Syst., Vol. 419, Springer Verlag, Berlin 1975, pp. 247259, corresponds in a canonical way to the adjoint of a linear operator associated to F. 1.
The Regions Below of Lipschitz Maps
"... Abstract: Let (X, d) be a compact metric space, we use ↓USC(X) and ↓LIP(X) to denote the family of the regions below of all upper semicontinuous maps and all Lipschitz maps from X to I = [0, 1], respectively. In this paper, we show that (↓USC(X), ↓LIP(X)) ≈ (Q, B(Q)), where B(Q) = Q \ (−1, 1)ω is ..."
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Abstract: Let (X, d) be a compact metric space, we use ↓USC(X) and ↓LIP(X) to denote the family of the regions below of all upper semicontinuous maps and all Lipschitz maps from X to I = [0, 1], respectively. In this paper, we show that (↓USC(X), ↓LIP(X)) ≈ (Q, B(Q)), where B(Q) = Q \ (−1, 1)ω
Lipschitz maps on trees
, 2000
"... Abstract. We introduce and study a metric notion for trees and relate it to a conjecture of Shelah [10] about the existence of a finite basis for a class of linear orderings. Contents ..."
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Cited by 4 (1 self)
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Abstract. We introduce and study a metric notion for trees and relate it to a conjecture of Shelah [10] about the existence of a finite basis for a class of linear orderings. Contents
ON THE EXTENSIONS OF HÖLDERLIPSCHITZ MAPS
"... If (X, d) and (Y, %) are metric spaces, α ∈ (0, 1] and K> 0, we say that a map f: X → Y is αHölder with constant K (or in short (K,α)Hölder) if ∀x, y ∈ X, %(f(x), f(y)) ≤ Kd(x, y)α. We refer to [2] for background and more information about Hölder maps. In [12] and [9] the following notation ..."
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If (X, d) and (Y, %) are metric spaces, α ∈ (0, 1] and K> 0, we say that a map f: X → Y is αHölder with constant K (or in short (K,α)Hölder) if ∀x, y ∈ X, %(f(x), f(y)) ≤ Kd(x, y)α. We refer to [2] for background and more information about Hölder maps. In [12] and [9] the following
Generating continuous mappings with Lipschitz mappings
 Trans. Amer. Math. Soc
"... Abstract. If X is a metric space then CX and LX denote the semigroups of continuous and Lipschitz mappings, respectively, from X to itself. The relative rank of CX modulo LX is the least cardinality of any set U \LX where U generates CX. For a large class of separable metric spaces X we prove that t ..."
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Cited by 10 (7 self)
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Abstract. If X is a metric space then CX and LX denote the semigroups of continuous and Lipschitz mappings, respectively, from X to itself. The relative rank of CX modulo LX is the least cardinality of any set U \LX where U generates CX. For a large class of separable metric spaces X we prove
EXTENDABILITY OF LARGESCALE LIPSCHITZ MAPS
, 1999
"... Abstract. Let X, Y be metric spaces, S a subset of X, and f: S → Y a largescale lipschitz map. It is shown that f possesses a largescale lipschitz extension ¯ f: X → Y (with possibly larger constants) if Y is a Gromov hyperbolic geodesic space or the cartesian product of finitely many such spaces. ..."
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Abstract. Let X, Y be metric spaces, S a subset of X, and f: S → Y a largescale lipschitz map. It is shown that f possesses a largescale lipschitz extension ¯ f: X → Y (with possibly larger constants) if Y is a Gromov hyperbolic geodesic space or the cartesian product of finitely many such spaces
Results 1  10
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749