Isometric imbeddings of Euclidean spaces into finite dimensional $l_p$-spaces

Isometric Embeddings of Snowflakes into Finite-dimensional Banach Spaces

We consider a general notion of snowflake of a metric space by composing the distance with a nontrivial concave function. We prove that a snowflake of a metric space X isometrically embeds into some finite-dimensional normed space if and only if X is finite. In the case of power functions we give a uniform bound on the cardinality of X depending only on the power exponent and the dimension of t...

Embedding non-Euclidean color spaces into Euclidean color spaces with minimal isometric disagreement.

Isometric embedding of non-Euclidean color spaces into Euclidean color spaces is investigated. Owing to regions of nonzero Gaussian curvature within common non-Euclidean color spaces, we focus on the determination of transformations into Euclidean spaces with minimal isometric disagreement. A computational method is presented for deriving such a color space transformation by means of a multigri...

Euclidean Structure in Finite Dimensional Normed Spaces

Windows into non-Euclidean spaces

Bilipschitz Embeddings of Metric Spaces into Euclidean Spaces

When does a metric space admit a bilipschitz embedding into some finite-dimensional Euclidean space? There does not seem to be a simple answer to this question. Results of Assouad [A1], [A2], [A3] do provide a simple answer if one permits some small (“snowflake”) deformations of the metric, but unfortunately these deformations immediately disrupt some basic aspects of geometry and analysis, lik...