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Counterexamples to Smoothing Convex Functions

Published online by Cambridge University Press:  20 November 2018

Patrick Adrian Neale Smith
Patrick Adrian Neale Smith*
Affiliation:
University of Toronto, TorontoOnt. M5S 1A1
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Abstract

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Greene and Wu have shown that any continuous strongly convex function on a Riemannian manifold can be uniformly approximated by infinitely differentiable strongly convex functions. This result is not true if the word “strongly” is omitted; in this paper, we give examples of manifolds on which convex functions cannot be approximated by convex functions (k = 0, 1,2,...).

Keywords

53C99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 3 , 01 September 1986 , pp. 308 - 313
Copyright
Copyright © Canadian Mathematical Society 1986

References

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