Constant T-curvature conformal metrics on 4-manifolds with boundary

• Autores: Cheikh Birahim Ndiaye
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 240, Nº 1, 2009, págs. 151-184
• Idioma: inglés
• DOI: 10.2140/pjm.2009.240.151
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• Resumen

  • In this paper we prove that, given a compact four-dimensional smooth Riemannian manifold (M,g) with smooth boundary, there exists a metric conformal to g with constant T-curvature, zero Q-curvature and zero mean curvature under generic and conformally invariant assumptions. The problem amounts to solving a fourth-order nonlinear elliptic boundary value problem (BVP) with boundary conditions given by a third-order pseudodifferential operator and homogeneous Neumann operator. It has a variational structure, but since the corresponding Euler�Lagrange functional is in general unbounded from below, we look for saddle points. We do this by using topological arguments and min-max methods combined with a compactness result for the corresponding BVP.