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On gluing Alexandrov spaces with lower Ricci curvature bounds

Differential Geometry 2020-03-16 v1 Metric Geometry

Abstract

In this paper we prove that in the class of metric measure spaces with Alexandrov curvature bounded from below the Riemannian curvature-dimension condition RCD(K,N)RCD(K,N) with KRK\in \mathbb{R} and N[1,)N\in [1,\infty) is preserved under doubling and gluing constructions.

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Cite

@article{arxiv.2003.06242,
  title  = {On gluing Alexandrov spaces with lower Ricci curvature bounds},
  author = {Vitali Kapovitch and Christian Ketterer and Karl-Theodor Sturm},
  journal= {arXiv preprint arXiv:2003.06242},
  year   = {2020}
}

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24 pages