Displaying similar documents to “Permanence of metric fractals.”

Poincaré Inequalities for Mutually Singular Measures

Andrea Schioppa (2015)

Analysis and Geometry in Metric Spaces

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Using an inverse system of metric graphs as in [3], we provide a simple example of a metric space X that admits Poincaré inequalities for a continuum of mutually singular measures.

A discrete version of the Brunn-Minkowski inequality and its stability

Michel Bonnefont (2009)

Annales mathématiques Blaise Pascal

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In the first part of the paper, we define an approximated Brunn-Minkowski inequality which generalizes the classical one for metric measure spaces. Our new definition, based only on properties of the distance, allows also us to deal with discrete metric measure spaces. Then we show the stability of our new inequality under convergence of metric measure spaces. This result gives as corollary the stability of the classical Brunn-Minkowski inequality for geodesic spaces. The proof of this...

Extension of Lipschitz functions defined on metric subspaces of homogeneous type.

Alexander Brudnyi, Yuri Brudnyi (2006)

Revista Matemática Complutense

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If a metric subspace Mº of an arbitrary metric space M carries a doubling measure μ, then there is a simultaneous linear extension of all Lipschitz functions on Mº ranged in a Banach space to those on M. Moreover, the norm of this linear operator is controlled by logarithm of the doubling constant of μ.

On the gluing of hyperconvex metrics and diversities

Bożena Piątek (2014)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In this work we consider two hyperconvex diversities (or hyperconvex metric spaces) (X, δX) and (Y, δY ) with nonempty intersection and we wonder whether there is a natural way to glue them so that the new glued diversity (or metric space) remains being hyperconvex. We provide positive and negative answers in both situations.