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Creators/Authors contains: "Wylie, William"

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  1. (, Letters in Mathematical Physics)
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  2. ; ; ; (, Differential Geometry and its Applications)
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  3. ; (, Differential Geometry and its Applications)
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  4. ; ; (, Letters in Mathematical Physics)
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  5. ; (, Journal of Geometry and Physics)
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  6. ; ; (, Calculus of Variations and Partial Differential Equations)
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  7. ; ; (, The Journal of Geometric Analysis)
    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. 
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  8. ; (, Indiana University Mathematics Journal)
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