Busemann and MCP

Abstract

We study the structure of Busemann spaces with measures satisfying the measure contraction property (MCP). The main results are rigidity theorems and structure theorems under the assumption of geodesic completeness or non-collapse. The appendix contains some observations on the tangent cones of geodesically complete Busemann spaces.

added a statement on the measure to Theorem 1.1, deleted Corollary 4.4, merged Remark 4.5 into Remark 1.2, added Remark 4.4, replaced Remark 3.6 with the proof of Proposition 3.5, added the proof of Corollary 5.10, added references, and made other minor changes