Lunes 16 de Octubre 2023 a las 12:00 hrs., Sala de Seminarios Piso 5, Beauchef 851

Speaker: Maria Fernanda Espinal Florez, (PUC).

Title: A gluing construction of singular solutions for a fully non-linear equation in conformal geometry.

Abstract: We study construction of a complete non-compact Riemannian metrics with positive constant σ2-curvature, on the sphere Sn with a prescribed singular set Λ given by a disjoint union of closed submanifolds whose dimension is positive and strictly less than n−√n−22 .

This is a fully non-linear problem, nevertheless, we show that the classical gluing method of Mazzeo-Pacard for the scalar curvature still works in this setting since the linearized operator has good mapping properties in weighted spaces. A necessary condition is that 2 ≤ 2k < n.

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