Abstracts of talks

Speaker: L. Battaglia (Roma Tre)
Title: Prescribing almost constant curvatures on the half-plane
Abstract: We consider the problem of prescribing both the Gaussian curvature in the half plane and the geodesic curvature on its boundary. We show the existence of solutions with non-constant curvatures bifurcating from the (explicitly known) solutions to the problem with constant curvatures. The main arguments used in proofs are finite-dimensional reduction and degree theory.
Joint works with M. Cozzi, A. Fernandez, A. Pistoia, S. Cruz-Blázquez.

Speaker: J.C Fernández-Morelos (UNAM)
Title: Optimal Partitions and prescribed Q-curvature equations
Abstract: We will study the optimal partition problem related to the prescribed Q-curvature equation defined for higher order conformal operators in a closed Riemannian manifold. Roughly speaking, the optimal partition problem consists in seeking a partition of a Riemannian manifold in subdomains in such a way that the average energy (induced by the higher order conformal operators) in these domains attains its minimum. We will see the close relation between the optimal partition problem and the existence of least energy solutions for weakly competitive systems of Q-curvature equations on manifolds. In order to get a concrete description of the domains solving the problem and their boundaries, we introduce suitable groups of symmetries acting on the manifold. This is a joint work with Mónica Clapp, Alberto Saldaña, Oscar Palmas and Jonatán Torres-Orozco from UNAM.