Extending metrics uniformly
Nguyen To Nhu (1980)
Colloquium Mathematicae
Similarity:
Nguyen To Nhu (1980)
Colloquium Mathematicae
Similarity:
Diethard Pallaschke, Dieter Pumplün (2015)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Similarity:
In this paper the universal properties of spaces of Lipschitz functions, defined over metric spaces, are investigated.
Nguyen Van Khue, Nguyen To Nhu (1981)
Colloquium Mathematicae
Similarity:
Janusz Matkowski, Małgorzata Wróbel (2012)
Open Mathematics
Similarity:
We show that the generator of any uniformly bounded set-valued Nemytskij composition operator acting between generalized Hölder function metric spaces, with nonempty, bounded, closed, and convex values, is an affine function.
Juutinen, Petri (2002)
Annales Academiae Scientiarum Fennicae. Mathematica
Similarity:
Giuseppe Marino (1998)
Extracta Mathematicae
Similarity:
K. Leśniak (2007)
Bulletin of the Polish Academy of Sciences. Mathematics
Similarity:
The Lifshits theorem states that any k-uniformly Lipschitz map with a bounded orbit on a complete metric space X has a fixed point provided k < ϰ(X) where ϰ(X) is the so-called Lifshits constant of X. For many spaces we have ϰ(X) > 1. It is interesting whether we can use the Lifshits theorem in the theory of iterated function systems. Therefore we investigate the value of the Lifshits constant for several classes of hyperspaces.
Gemma Piella (2023)
Applications of Mathematics
Similarity:
Distance metrics are at the core of many processing and machine learning algorithms. In many contexts, it is useful to compute the distance between data using multiple criteria. This naturally leads to consider vector-valued metrics, in which the distance is no longer a real positive number but a vector. In this paper, we propose a principled way to combine several metrics into either a scalar-valued or vector-valued metric. We illustrate our framework by reformulating the popular structural...
Jeff Cheeger, Bruce Kleiner, Andrea Schioppa (2016)
Analysis and Geometry in Metric Spaces
Similarity:
We prove metric differentiation for differentiability spaces in the sense of Cheeger [10, 14, 27]. As corollarieswe give a new proof of one of the main results of [14], a proof that the Lip-lip constant of any Lip-lip space in the sense of Keith [27] is equal to 1, and new nonembeddability results.
J. Wilker (1971)
Fundamenta Mathematicae
Similarity:
H. Herold (1985)
Publications de l'Institut Mathématique
Similarity:
Jan Hubička, Matěj Konečný, Jaroslav Nešetřil (2019)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces.
David M. Freeman (2014)
Analysis and Geometry in Metric Spaces
Similarity:
We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the J2-condition, thus characterizing a special case of inversion invariant bi-Lipschitz homogeneity. A more general characterization of inversion invariant bi-Lipschitz homogeneity for certain non-fractal metric spaces is also provided.
Immo Hahlomaa (2005)
Fundamenta Mathematicae
Similarity:
We show that pointwise bounds on the Menger curvature imply Lipschitz parametrization for general compact metric spaces. We also give some estimates on the optimal Lipschitz constants of the parametrizing maps for the metric spaces in Ω(ε), the class of bounded metric spaces E such that the maximum angle for every triple in E is at least π/2 + arcsinε. Finally, we extend Peter Jones's travelling salesman theorem to general metric spaces.
Sean Li (2015)
Analysis and Geometry in Metric Spaces
Similarity:
Let f : G → H be a Lipschitz map between two Carnot groups. We show that if B is a ball of G, then there exists a subset Z ⊂ B, whose image in H under f has small Hausdorff content, such that BZcan be decomposed into a controlled number of pieces, the restriction of f on each of which is quantitatively biLipschitz. This extends a result of [14], which proved the same result, but with the restriction that G has an appropriate discretization. We provide an example of a Carnot group not...
Robert Fraser (1969)
Studia Mathematica
Similarity:
Rieffel, Marc A. (1999)
Documenta Mathematica
Similarity: