6533b7defe1ef96bd1275e1a
RESEARCH PRODUCT
Failure of the local-to-global property for CD(K,N) spaces
Tapio Rajalasubject
Mathematics - Differential GeometryDiscrete mathematicsProperty (philosophy)GeodesicLebesgue measureExistential quantification010102 general mathematicsMetric Geometry (math.MG)Space (mathematics)01 natural sciencesMeasure (mathematics)Theoretical Computer ScienceMathematics (miscellaneous)Mathematics - Metric GeometryDifferential Geometry (math.DG)0103 physical sciencesMetric (mathematics)FOS: Mathematics010307 mathematical physics0101 mathematics53C23 (Primary) 28A33 49Q20 (Secondary)Mathematicsdescription
Given any K and N we show that there exists a compact geodesic metric measure space satisfying locally the CD(0,4) condition but failing CD(K,N) globally. The space with this property is a suitable non convex subset of R^2 equipped with the l^\infty-norm and the Lebesgue measure. Combining many such spaces gives a (non compact) complete geodesic metric measure space satisfying CD(0,4) locally but failing CD(K,N) globally for every K and N.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-02-25 | ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE |