Moderate smoothness of most Alexandrov surfaces

Jin-ichi Itoh; Joel Rouyer; Costin Vilcu

Moderate smoothness of most Alexandrov surfaces

Metric Geometry 2014-05-20 v2

Authors: Jin-ichi Itoh , Joel Rouyer , Costin Vilcu

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.

Keywords

alexandrov surfaces curvature bounded below baire category conical points gaussian curvature

Cite

@article{arxiv.1308.3862,
  title  = {Moderate smoothness of most Alexandrov surfaces},
  author = {Jin-ichi Itoh and Joel Rouyer and Costin Vilcu},
  journal= {arXiv preprint arXiv:1308.3862},
  year   = {2014}
}