The Scalar Curvature Problem on the Four Dimensional Half Sphere

Details The Scalar Curvature Problem on the Four Dimensional Half Sphere The Scalar Curvature Problem on the Four Dimensional Half Sphere

2003-03-04

arxiv.org/abs/math/0303039v4

Mathematics

Analysis of PDEs

19 pages

Scientific paper

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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