Manifolds with wells of negative curvature (with an Appendix by Daniel Ruberman).
Inventiones mathematicae, Tome 103 (1991) no. 1, pp. 471-496.

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Mots-clés : obstructions for metrics with positivity of curvature, vanishing theorem, cohomology, shallow wells of negative curvature, Laplacian
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     title = {Manifolds with wells of negative curvature (with an {Appendix} by {Daniel} {Ruberman).}},
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K.D. Elworthy; Steven Rosenberg. Manifolds with wells of negative curvature (with an Appendix by Daniel Ruberman).. Inventiones mathematicae, Tome 103 (1991) no. 1, pp. 471-496. http://geodesic.mathdoc.fr/item/IM_1991__103_1_143866/