6533b7cffe1ef96bd1259033

RESEARCH PRODUCT

Failure of topological rigidity results for the measure contraction property

Tapio RajalaChristian Ketterer

subject

Mathematics - Differential Geometrymetric measure spacesGeodesicPhysics::Instrumentation and DetectorsQuantitative Biology::Tissues and Organsmeasure contraction propertyMetric Geometry (math.MG)53C23 (Primary) 28A33 49Q20 (Secondary)Ricci curvature lower boundsTopologyPotential theorymaximal diameter theoremnonbranchingRigidity (electromagnetism)Mathematics - Metric GeometryDifferential Geometry (math.DG)splitting theoremFOS: MathematicsSplitting theoremContraction (operator theory)AnalysisMathematicsgeodesics

description

We give two examples of metric measure spaces satisfying the measure contraction property MCP(K,N) but having different topological dimensions at different regions of the space. The first one satisfies MCP(0,3) and contains a subset isometric to $\mathbb{R}$, but does not topologically split. The second space satisfies MCP(2,3) and has diameter $\pi$, which is the maximal possible diameter for a space satisfying MCP(N-1,N), but is not a topological spherical suspension. The latter example gives an answer to a question by Ohta.

yearjournalcountryeditionlanguage
2014-03-12
https://dx.doi.org/10.48550/arxiv.1403.3105