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The Scalar Curvature Problem on the Four Dimensional Half Sphere

M. Ben Ayed·K. El Mehdi·M. Ould Ahmedou
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Abstract

In this paper, we consider the problem of prescribing the scalar curvature under minimal boundary conditions on the standard four dimensional half sphere. We provide an Euler-Hopf type criterion for a given function to be a scalar curvature to a metric conformal to the standard one. Our proof involves the study of critical points at infinity of the associated variational problem.

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M. Ben Ayed, K. El Mehdi, M. Ould Ahmedou. 2003-06-04. The Scalar Curvature Problem on the Four Dimensional Half Sphere. https://arxiv.org/abs/math/0303039

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