Moderate smoothness of most Alexandrov surfaces

Abstract

We show that, in the sense of Baire category, most Alexandrov surfaces with curvature bounded below by $\kappa$ have no conical points. We use this result to prove that at most points of such surfaces, the lower and the upper Gaussian curvatures are equal to $\kappa$ and $\infty$ respectively.

12 pages, 1 figure. Minor changes for the second version, mainly of linguistic nature