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Finite Energy Solutions to the Yamabe Equation

Authors:

Qi S. Zhang

Affiliation:

(1) Department of Mathematics, University of California, Riverside, CA, 92521, U.S.A.

Abstract:

We prove the existence of positive, finite energy solutions to the Yamabe equation

$Delta u - frac{{n - 2}}{{4(n - 1)}}Su + u^{(n + 2)/(n - 2)} = 0$

on some noncompact manifolds with positive scalar curvature. We also clarify a published result on the existence of 'complete solutions' on those manifolds.

Keywords:

noncompact Yamabe problem

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