On Projections of Metric Spaces

DOI10.20382/JOCG.V5I1A13arXiv1106.4910MaRDI QIDQ6226214

Author name not available (Why is that?)

Publication date: 24 June 2011

Abstract: Let $X$ be a metric space and let $mu$ be a probability measure on it. Consider a Lipschitz map $T:XightarrowRn$, with Lipschitz constant $leq1$. Then one can ask whether the image $TX$ can have large projections on many directions. For a large class of spaces $X$, we show that there are directions $phiinsphere$ on which the projection of the image $TX$ is small on the average, with bounds depending on the dimension $n$ and the eigenvalues of the Laplacian on $X$.

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