TL;DR
This paper investigates the structure of Busemann spaces with measures satisfying the measure contraction property, establishing rigidity and structure theorems under certain conditions.
Contribution
It provides new rigidity and structure theorems for Busemann spaces with MCP, especially under geodesic completeness or non-collapse assumptions.
Findings
Rigidity theorems for Busemann spaces with MCP
Structure theorems under geodesic completeness
Observations on tangent cones of geodesically complete spaces
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.
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