Geodesic
Counterexamples to Smoothing Convex Functions
Canadian mathematical bulletin, Tome 29 (1986) no. 3, pp. 308-313

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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,...).
DOI : 10.4153/CMB-1986-047-5
Mots-clés : 53C99 
Smith, Patrick Adrian Neale. Counterexamples to Smoothing Convex Functions. Canadian mathematical bulletin, Tome 29 (1986) no. 3, pp. 308-313. doi: 10.4153/CMB-1986-047-5
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     title = {Counterexamples to {Smoothing} {Convex} {Functions}},
     journal = {Canadian mathematical bulletin},
     pages = {308--313},
     year = {1986},
     volume = {29},
     number = {3},
     doi = {10.4153/CMB-1986-047-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-047-5/}
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