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Spectral Calculus and Lipschitz Extension for Barycentric Metric Spaces

100%

Mendel M., Naor A.

Analysis and Geometry in Metric Spaces

2013

tom 1

163-199

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.

On the Hausdorff dimension of ultrametric subsets in ℝⁿ

81%

Lee J., Mendel M., Moharrami M.

Fundamenta Mathematicae

2012

tom 218

nr 3

285-290

For every ε > 0, any subset of ℝⁿ with Hausdorff dimension larger than (1-ε)n must have ultrametric distortion larger than 1/(4ε).

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Fundamenta Mathematicae

2 Mendel M.

1 Lee J.

1 Moharrami M.

1 Naor A.

1 2013

1 2012

Wyniki wyszukiwania

Spectral Calculus and Lipschitz Extension for Barycentric Metric Spaces

On the Hausdorff dimension of ultrametric subsets in ℝⁿ