Communications in Analysis and Geometry

Volume 31 (2023)

Number 6

On gluing Alexandrov spaces with lower Ricci curvature bounds

Pages: 1529 – 1564

DOI: https://dx.doi.org/10.4310/CAG.2023.v31.n6.a6

Authors

Vitali Kapovitch (Department of Mathematics, University of Toronto, Ontario, Canada)

Christian Ketterer (Department of Mathematics, University of Toronto, Ontario, Canada)

Karl-Theodor Sturm (Institute for Applied Mathematics, University of Bonn, Germany)

Abstract

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

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VK is partially supported by a Discovery grant from NSERC. CK is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Projektnummer 396662902. KTS gratefully acknowledges financial support by the European Union through the ERC-AdG “RicciBounds” and by the DFG through the Excellence Cluster “Hausdorff Center for Mathematics” and through the Collaborative Research Center 1060.

Received 20 April 2020

Accepted 10 June 2021

Published 9 August 2024