Weakly Noncollapsed RCD Spaces with Upper Curvature Bounds

Abstract

We show that if a CD(K, n) space (X, d, f ℋn) with n ≥ 2 has curvature bounded above by κ in the sense of Alexandrov then f is constant.

Keywords

• riemannian curvature-dimension condition
• upper curvature bound
• alexandrov space
• optimal transport
• 53c20
• 53c21