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Curvature properties of typical convex surfaces. (English) Zbl 0637.52005
Refining and extending earlier results of himself [e.g., Math. Ann. 252, 217-219 (1980; Zbl 0427.53002)] and others, the author proves some more properties of “typical” convex surfaces (in the sense of Baire category). An easily formulated example says that on a typical convex curve in the plane the curvature is zero almost everywhere and infinite at an uncountable dense set of points. Higher-dimensional results deal with the behaviour of sectional curvatures in certain directions and also establish the fact a typical convex surface is, in a certain sense, almost everywhere very close to its tangent hyperplane.
Reviewer: R.Schneider

##### MSC:
 52A20 Convex sets in $$n$$ dimensions (including convex hypersurfaces) 52A10 Convex sets in $$2$$ dimensions (including convex curves)
##### Keywords:
typical convex surface; Baire category; curvature
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