On Projections of Metric Spaces

Details On Projections of Metric Spaces On Projections of Metric Spaces

2011-06-24

arxiv.org/abs/1106.4910v1

Mathematics

Functional Analysis

Scientific paper

Let $X$ be a metric space and let $\mu$ be a probability measure on it. Consider a Lipschitz map $T: X \rightarrow \Rn$, with Lipschitz constant $\leq 1$. 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 $\phi \in \nsphere$ 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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