Seminario de Geometría (virtual)

Event Details

Día: 16 de octubre de 2020
Hora: 13:00 - 14:00
Lugar: Videoconferencia Sala TESLA de UGR,
Contraseña de la reunión: 576333
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Ponente: Jorge Lira (Universidad de Fortaleza, Brasil)
Título: Einstein type elliptic systems

Resumen: We will discuss a type of semi-linear systems of partial differential equations which are motivated by the conformal formulation of the Einstein constraint equations coupled with realistic physical fields on asymptotically flat manifolds. In particular, electromagnetic fields give rise to this kind of systems. In this context, under suitable conditions, we prove a general existence theorem for such systems, and, in particular, under smallness assumptions on the free parameters of the problem, we prove existence of far from CMC (near CMC) Yamabe positive (Yamabe non-positive) solutions for charged dust coupled to the Einstein equations, satisfying a trapped surface condition on the boundary. As a bypass, we prove a Helmholtz decomposition on asymptotically flat manifolds with boundary, which extends and clarifies previously known results.
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