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Nonuniform thickness and weighted distance
Journal article   Open access   Peer reviewed

Nonuniform thickness and weighted distance

Oguz C Durumeric
Topology and its applications, Vol.156(8), pp.1578-1608
2009
DOI: 10.1016/j.topol.2009.01.008
url
https://doi.org/10.1016/j.topol.2009.01.008View
Published (Version of record) Open Access

Abstract

Nonuniform tubular neighborhoods of curves in R n 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.
Nonuniform thickness Normal injectivity radius Weighted distance

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