This is an announcement for the paper "A note on curves equipartition" by M. A. Lopez and S. Reisner.
Abstract: The problem of the existence of an equi-partition of a curve in $\R^n$ has recently been raised in the context of computational geometry. The problem is to show that for a (continuous) curve $\Gamma : [0,1] \to \R^n$ and for any positive integer $N$, there exist points $t_0=0<t_1<...<t_{N-1}<1=t_N$, such that $d(\Gamma(t_{i-1}),\Gamma(t_i))=d(\Gamma(t_{i}),\Gamma(t_{i+1}))$ for all $i=1,...,N$, where $d$ is a metric or even a semi-metric (a weaker notion) on $\R^n$. We show here that the existence of such points, in a much broader context, is a consequence of Brower's fixed point theorem.
Archive classification: math.FA math.CA
Mathematics Subject Classification: 58C30; 47H10
The source file(s), equipartition.tex: 10551 bytes, is(are) stored in gzipped form as 0707.4296.gz with size 4kb. The corresponding postcript file has gzipped size 46kb.
Submitted from: reisner@math.haifa.ac.il
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