This is an addendum to the paper [K. Bacher, K.T. Sturm, Localization and tensorization properties of the curvature-dimension condition for metric measure spaces, J. Funct. Anal. 259 (2010) 28-56]. We prove the tensorization property for the curvature-dimension condition, add some detailed calculations -including explicit dependence of constants -and comment on assumptions and conjectures concerning the local-toglobal statement in Bacher and Sturm (2010) [1] and Villani (2009) [6], respectively.
In this paper, we consider a complete noncompact n-submanifold M with parallel mean curvature vector h in an Euclidean space. If M has finite total curvature, we prove that M must be minimal, so that M is an affine n-plane if it is strongly stable. This is a generalization of the result on strongly stable complete hypersurfaces with constant mean curvature in R n+1 .
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