On the non-uniqueness of conformal metrics with prescribed scalar and mean curvatures on compact manifolds with boundary
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Gonzalo García [1] ; Jhovanny Munoz [1]
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[1] Universidad del Valle
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- Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 53, Nº. 1, 2012, págs. 29-42
- Idioma: inglés
- Enlaces
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Resumen
For a compact Riemannian manifold (Mn,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 g' < g with curvatures Rg' = Rg and hg' = hg. Furthermore, we establish the uniqueness of such a metric g' in the conformal class of the metric g when Rg ≥ 0.
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