Nonuniform thickness and weighted distance |
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Authors: | Oguz C Durumeric |
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Institution: | Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA |
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Abstract: | Nonuniform tubular neighborhoods of curves in Rn 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. |
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Keywords: | primary 57M25 53A04 53C21 53C20 secondary 58E30 |
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