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Hypersurfaces of extremal slope

Published online by Cambridge University Press:  12 July 2007

J. H. Rieger
J. H. Rieger
Affiliation:
Institut für Algebra und Geometrie, Martin-Luther-Universität Halle, D-06099 Halle, Germany (rieger@mathematik.uni-halle.de)
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Abstract

The hypersurface of extremal slope consists of extrema of the gradient magnitude along integral curves of the gradient vector field of a smooth function. We study the singularities, and other geometric features, of hypersurfaces of extremal slope associated with generic functions and with one-parameter families of functions representing generic solutions to the heat equation.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 2 , April 2003 , pp. 449 - 465
Copyright
Copyright © Royal Society of Edinburgh 2003

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