Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-05T14:40:23.224Z Has data issue: false hasContentIssue false
  • English
  • Français

The Rank Theorem for Locally Lipschitz Continuous Functions

Published online by Cambridge University Press:  20 November 2018

G. J. Butler ,
J. G. Timourian  and
C. Viger
G. J. Butler
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Albert T6G 2G1
J. G. Timourian
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Albert T6G 2G1
C. Viger
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Albert T6G 2G1
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The Rank Theorem is proved for locally Lipschitz continuous functions f:Rn → Rp with generalized derivative of constant rank.

Keywords

Rank TheoremLipschitz49A5252A99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 2 , 01 June 1988 , pp. 217 - 226
Copyright
Copyright © Canadian Mathematical Society 1988

References

1. Auslender, A., Theorem of constant rank for Lipschitzian maps, Mathematical programming with data perturbation, II, Lecture Notes in Pure and Appl. Math. 85, Dekker, New York, 1983, pp. 1–6.Google Scholar
2. Cheeger, J. and Kister, J. M., Counting topological manifolds, Topology 9 (1970), pp. 149–151.Google Scholar
3. Church, P. T. and Timourian, J. G., Differentiate maps with ^-dimensional critical set I, Pacific J. Math. (3) 41 (1972), pp. 615–629.Google Scholar
4. Church, P. T. and Timourian, J. G., Differentiable maps with ^-dimensional critical set II, Indiana University Math. J., 24 (1974), pp. 17–28.Google Scholar
5. Church, P. T. and Timourian, J. G., Fiberbundles with singularities, J. Math. Mech. 18 (1968), pp. 71–90.Google Scholar
6. Clarke, F. H., Optimization and Nonsmooth Analysis, CMS Monograph, Wiley-Interscience, New York, 1983.Google Scholar
7. Fédérer, H., Geometric Measure Theory, Springer-Verlag, New York, 1969.Google Scholar
8. Glick, N. and Ungar, P., Problems and solutions, American Math. Monthly 89 (1982), p. 133.Google Scholar
9. Milnor, J., Singular points of complex hyp ersurfaces, Annals of Math. Studies No. 61, Princeton Univ. Press, Princeton, N.J., 1968.Google Scholar
10. Nathan, W. D., Open mapping on manifolds, Ph.D. dissertation, Syracuse University, 1968.Google Scholar
11. Pourciau, B. H., Global properties of proper Lipschitzian maps, Siam J. Math. Anal. 14 (1983), pp. 796–799.Google Scholar
12. Timourian, J. G., Fiber bundles with discrete singular set, J. Math, and Mech. 18 (1968), pp. 61–70.Google Scholar
13. Timourian, J. G., Maps with discrete branch sets between manifolds of codimension one, Canadian J. Math. 21 (1969), pp. 660–668.Google Scholar