The scalar curvature equation on 2- and 3-spheres

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Abstract

In this article we obtain a priori estimates for solutions to the prescribed scalar curvature equation on 2- and 3-spheres under a nondegeneracy assumption on the curvature function. Using this estimate, we use the continuity method to demonstrate the existence of solutions to this equation when a map associated to the given curvature function has non-zero degree.

Research of first author supported in part by NSF grant 91-03949
Research of second author supported by a NSF Postdoctoral Fellowship.
Research of third author supported in part by NSF grant 91-02872 and the Ellentuck Fund.