Nonuniform Thickness and Weighted Distance

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dc.creatorDurumeric, Oguz C.
dc.date2007-05-16
dc.date2008-08-27
dc.date.accessioned2026-07-07T09:58:19Z
dc.date.available2026-07-07T09:58:19Z
dc.descriptionNonuniform tubular neighborhoods of curves in Euclidean n-space are studied by using weighted distance functions and generalizing the normal exponential map. Different notions of injectivity radii are introduced to investigate singular but injective exponential maps. A generalization of the thickness formula is obtained for nonuniform thickness. All singularities within almost injectivity radius are classified by the Horizontal Collapsing Property. Examples are provided to show the distinction between the different types of injectivity radii, as well as showing that the standard differentiable injectivity radius fails to be upper semicontinuous on a singular set of weight functions.
dc.identifierhttps://arxiv.org/abs/0705.2407
dc.identifierhttp://arxiv.org/abs/0705.2407
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167672
dc.subjectGeometric Topology
dc.subjectDifferential Geometry
dc.subject57M25; 53A04
dc.titleNonuniform Thickness and Weighted Distance
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