Connected sum constructions for constant scalar curvature metrics
Keywords
noncompact manifolds with constant scalar curvature, gluing, nondegeneracy hypothesis, connected sums, Schoen's construction, metrics with prescribed asymptoticsAbstract
We give a general procedure for gluing together possibly noncompact manifolds of constant scalar curvature which satisfy an extra nondegeneracy hypothesis. Our aim is to provide a simple paradigm for making "analytic" connected sums. In particular, we can easily construct complete metrics of constant positive scalar curvature on the complement of certain configurations of an even number of points on the sphere, which is a special case of Schoen's [S1] well-known, difficult construction. Applications of this construction produces metrics with prescribed asymptotics. In particular, we produce metrics with cylindrical ends, the simplest type of asymptotic behaviour. Solutions on the complement of an infinite number of points are also constructed by an iteration of our construction.Downloads
Published
1995-12-01
How to Cite
1.
MAZZEO, Rafe, POLLACK, Daniel and UHLENBECK, Karen. Connected sum constructions for constant scalar curvature metrics. Topological Methods in Nonlinear Analysis. Online. 1 December 1995. Vol. 6, no. 2, pp. 207 - 233. [Accessed 24 September 2024].
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