Rigidity for positively curved Alexandrov spaces with boundary

Abstract

Inspired by a recent work of Grove and Petersen (Alexandrov spaces with maximal radius, 2018), where the authors studied positively curved Alexandrov spaces with largest possible boundary, namely the round sphere, we study Alexandrov spaces with lower curvature bound 1 and with large boundary other than the sphere. In particular, we classify those spaces with radius equal to $$\pi /2$$ , and the intrinsic diameter of their boundaries is at most $$\pi /2$$ .