The connected components of the space of Alexandrov surfaces

Abstract

Denote by $\mathcal{A}(\kappa )$ the set of all compact Alexandrov surfaces with curvature bounded below by $\kappa$ without boundary, endowed with the topology induced by the Gromov-Hausdorff metric. We determine the connected components of $\mathcal{A}(\kappa )$ and of its closure.