Notes on the relative Yamabe invariant

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  • Differential Geometry : Proceedings of the First Intenational Symposiumu on Differential Geometry, February 22-24, 2001 Josai University

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The Yamabe invariant [K], [S2] of a closed smooth manifold X is a naturaldifferential-topological invariant which arises from a variational problem for the totalscalar curvature of Riemannian metrics on X. The relative Yamabe invariant [ABl] ofa compact connected smooth manifold W with nonempty boundary is a natural relativeversion of the Yamabe invariant of X. Hence the relative Yamabe invariant has severalfundamental properties analogous to the corresponding ones for the classic Yamabe invariant.In particular, in respect of surgery on X and the interior of W, these two invariantshave quite similar properties. In this article, we give those properties.

Differential Geometry : Proceedings of the First Intenational Symposiumu on Differential Geometry, February 22-24, 2001 Josai University, edited by Qing-Ming Cheng. Dedicated to Professor Katsuhiro Shiohama on his sixtieth birthday.

identifier:JOS-KJ00000229300

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