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Nonuniform Thickness and Weighted Distance
by
Oguz C Durumeric
University of Iowa
Non-uniform tubular neighborhoods of submanifolds of the Euclidean space 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 non-uniform thickness. All singularities within almost injectivity radius in dimension 1 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.
Paper reference: arXiv:0705.2407
Date received: February 12, 2008
Copyright © 2008 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cawt-02.