Projecting (n − 1)-cycles to Zero on Hyperplanes in R N+1
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چکیده
The projection of a compact oriented submanifold M ⊂ R n+1 on a hyperplane P n can fail to bound any region in P . We call this “projecting to zero.” Example: The equatorial S ⊂ S ⊂ R projects to zero in any plane containing the x3-axis. Using currents to make this precise, we show: A lipschitz (homology) (n − 1)-sphere embedded in a compact, strictly convex hypersurface cannot project to zero on n+1 linearly independent hyperplanes in R . We also show, using examples, that all the hypotheses in this statement are sharp.
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تاریخ انتشار 2002