From volume cone to metric cone in the nonsmooth setting

Abstract

We prove that `volume cone implies metric cone' in the setting of RCD spaces, thus generalising to this class of spaces a well known result of Cheeger-Colding valid in Ricci-limit spaces.

References in corpus (1)

• Sobolev spaces on warped products

Cited by in corpus (4)

• Local spectral convergence in $RC{D}^{\ast }(K,N)$ spaces
• Cheeger-Colding-Tian theory for conic Kahler-Einstein metrics
• A Bishop type inequality on metric measure spaces with Ricci curvature bounded below
• Noncompact RCD(0,N) spaces with linear volume growth