比利时vs摩洛哥足彩
,
university of california san diego
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geometric analysis seminar
raanan schul
ucla
bi-lipschitz decomposition of lipschitz functions into a metric space.
abstract:
we will outline the proof of a quantitative version of the following sard type theorem. given a lipschitz function $f$ from the $k-$dimensional unit cube into a general metric space, one can decomposed $f$ into a finite number of bi-lipschitz functions $f|_{f_i}$ so that the $k-$hausdorff content of $f([0, 1]^k \smallsetminus \cup f_i$) is small. the case where the metric space is $\mathbb{r}^d$ is a theorem of p. jones (1988). this positively answers problem 11.13 in ``fractured fractals and broken dreams" by g. david and s. semmes, or equivalently, question 9 from ``thirty-three yes or no questions about mappings, measures, and metrics" by j. heinonen and s. semmes.
sponsor: kate okikiolu
february 3, 2009
1:00 pm
ap&m 6402
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