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.
We show that the theorem of the three perpendiculars holds in any n-dimensional space form.
We extend the notion of a source unfolding of a convex polyhedron P to be based on a closed polygonal curve Q in a particular class rather than based on a point. The class requires that Q lives on a cone to both sides; it includes simple, closed quas
igeodesics. Cutting a particular subset of the cut locus of Q (in P) leads to a non-overlapping unfolding of the polyhedron. This gives a new general method to unfold the surface of any convex polyhedron to a simple, planar polygon.
