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- W2964304966 abstract "In this paper we study sectional curvature bounds for Riemannian manifolds with density from the perspective of a weighted torsion-free connection introduced recently by the last two authors. We develop two new tools for studying weighted sectional curvature bounds: a new weighted Rauch comparison theorem and a modified notion of convexity for distance functions. As applications we prove generalizations of theorems of Preissman and Byers for negative curvature, the (homeomorphic) quarter-pinched sphere theorem, and Cheeger’s finiteness theorem. We also improve results of the first two authors for spaces of positive weighted sectional curvature and symmetry." @default.
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- W2964304966 date "2018-04-24" @default.
- W2964304966 modified "2023-09-23" @default.
- W2964304966 title "The Weighted Connection and Sectional Curvature for Manifolds With Density" @default.
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- W2964304966 doi "https://doi.org/10.1007/s12220-018-0025-3" @default.
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