Wyniki wyszukiwania

1

Tight Embeddability of Proper and Stable Metric Spaces

100%

Baudier F., Lancien G.

Analysis and Geometry in Metric Spaces

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2015

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tom 3

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nr 1

EN

We introduce the notions of almost Lipschitz embeddability and nearly isometric embeddability. We prove that for p ∈ [1,∞], every proper subset of Lp is almost Lipschitzly embeddable into a Banach space X if and only if X contains uniformly the ℓpn’s. We also sharpen a result of N. Kalton by showing that every stable metric space is nearly isometrically embeddable in the class of reflexive Banach spaces.

2

On Asymmetric Distances

76%

Mennucci A. C. G.

Analysis and Geometry in Metric Spaces

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2013

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tom 1

200-231

EN

In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize the setting of General metric spaces of Busemann, and discuss the newly found aspects of the theory: we identify three interesting classes of paths, and compare them; we note that a geodesic segment (as defined by Busemann) is not necessarily continuous in our setting; hence we present three different notions of intrinsic metric space.

3

Spectral Calculus and Lipschitz Extension for Barycentric Metric Spaces

76%

Mendel M., Naor A.

Analysis and Geometry in Metric Spaces

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2013

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tom 1

163-199

EN

The metric Markov cotype of barycentric metric spaces is computed, yielding the first class of metric spaces that are not Banach spaces for which this bi-Lipschitz invariant is understood. It is shown that this leads to new nonlinear spectral calculus inequalities, as well as a unified framework for Lipschitz extension, including new Lipschitz extension results for CAT (0) targets. An example that elucidates the relation between metric Markov cotype and Rademacher cotype is analyzed, showing that a classical Lipschitz extension theorem of Johnson, Lindenstrauss and Benyamini is asymptotically sharp.

Ograniczanie wyników

3 Analysis and Geometry in Metric Spaces

1 Baudier F.

1 Lancien G.

1 Mendel M.

1 Mennucci A. C. G.

1 Naor A.

1 2015

2 2013

Tight Embeddability of Proper and Stable Metric Spaces

On Asymmetric Distances

Spectral Calculus and Lipschitz Extension for Barycentric Metric Spaces