Projecting (n-1)-cycles to zero on hyperplanes in R^{n+1}

dc.creator	Solomon, Bruce
dc.date	2002-09-18
dc.date.accessioned	2026-07-07T04:50:58Z
dc.date.available	2026-07-07T04:50:58Z
dc.description	The projection of a compact oriented submanifold M^{n-1} in 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^1 in S^2 projects to zero in any plane containing the x_3-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^{n+1}. We also show, using examples, that all the hypotheses in this statement are sharp.
dc.description	14 pages, 4 figures
dc.identifier	https://arxiv.org/abs/math/0209226
dc.identifier	http://arxiv.org/abs/math/0209226
dc.identifier.uri	http://salesiana.dossiersoluciones.com/handle/123456789/64985
dc.subject	Differential Geometry
dc.subject	53A07; 53C42; 49Q15
dc.title	Projecting (n-1)-cycles to zero on hyperplanes in R^{n+1}
dc.type	text

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