On the Non-uniqueness of Conformal Metrics with Prescribed Scalar and Mean Curvatures on Compact Manifolds with Boundary
نویسندگان
چکیده
For a compact Riemannian manifold (M, g) with boundary and dimension n, with n ≥ 2, we study the existence of metrics in the conformal class of g with scalar curvature Rg and mean curvature hg on the boundary. In this paper we find sufficient and necessary conditions for the existence of a smaller metric g̃ < g with curvatures Rg̃ = Rg and hg̃ = hg. Furthermore, we establish the uniqueness of such a metric g̃ in the conformal class of the metric g when Rg ≥ 0.
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