6533b7d8fe1ef96bd1269b21
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Euclidean spaces as weak tangents of infinitesimally Hilbertian metric spaces with Ricci curvature bounded below
Andrea MondinoNicola GigliTapio Rajalasubject
Mathematics - Differential GeometryPure mathematicsGeneral MathematicsSpace (mathematics)01 natural sciencesMeasure (mathematics)Mathematics - Metric Geometry0103 physical sciencesFOS: MathematicsMathematics::Metric Geometry0101 mathematics[MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG]tangent spaces; non-smooth geometryRicci curvatureMathematics51F99-53B99non-smooth geometrySequenceEuclidean spaceApplied MathematicsHilbertian spaces010102 general mathematicstangent spacesTangentMetric Geometry (math.MG)Euclidean spacesDifferential Geometry (math.DG)[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]weak tangentsBounded functionSplitting theorem010307 mathematical physicsdescription
We show that in any infinitesimally Hilbertian CD* (K,N)-space at almost every point there exists a Euclidean weak tangent, i.e., there exists a sequence of dilations of the space that converges to Euclidean space in the pointed measured Gromov-Hausdorff topology. The proof follows by considering iterated tangents and the splitting theorem for infinitesimally Hilbertian CD* (0,N)-spaces.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-04-19 |