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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The Dirac operator on spaces with conical singularities and positive scalar curvatures


Author: Arthur Weichung Chou
Journal: Trans. Amer. Math. Soc. 289 (1985), 1-40
MSC: Primary 58G10; Secondary 58G05, 58G11, 58G25
MathSciNet review: 779050
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Abstract: We study, in the spirit of Jeff Cheeger, the Dirac operator on a space with conical singularities. We obtain a Bochner-type vanishing theorem and prove an index theorem in the singular case. Also, the relationship with manifolds with boundary is explored. In the Appendix two methods of deforming the metric near the boundary are established and applied to obtain several new results on constructing complete metrics with positive scalar curvature.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0779050-8
Article copyright: © Copyright 1985 American Mathematical Society