Abstract
In the sense of Baire categories, most convex curves on a smooth twodimensional closed convex surface are smooth. Moreover, if the set of all closed geodesics has empty interior in the space of all convex curves, then most convex curves are strictly convex.
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This paper was written during the author's visit at Western Washington University, whose substantial support is acknowledged.
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Zamfirescu, T. Typical convex curves on convex surfaces. Monatshefte für Mathematik 103, 241–247 (1987). https://doi.org/10.1007/BF01364343
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DOI: https://doi.org/10.1007/BF01364343