Seminario EDP UAM-ICMAT
Prescribing symmetric Q and T curvatures on the four-dimensional upper hemisphere
Ponente: Sergio Cruz Blázquez (UAM)Fecha: viernes 07 de marzo de 2025 - 12:15Lugar: Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Resumen:
We address the problem of prescribing non-constant Q and boundary T curvature on the four-dimensional upper hemisphere via a conformal change of the background metric. This is equivalent to solve a fourth-order non-linear elliptic boundary value problem with a third-order non-linear equation and homogeneous Neumann conditions at the boundary. The problem admits a Mean-field type variational formulation, with the associated energy functional being bounded from below but, in general, not coercive. By imposing symmetry conditions, we are able to prove the existence of minimizers, especially when Q, T ≥ 0.
This is a joint work with Azahara DeLaTorre, from Sapienza University of Rome.
