Seminario de Geometría

Detalles de Evento

Conferenciante: Esko Heinonem (Universidad de Helsinki)
Título: "Asymptotic Dirichlet problems for the mean curvature operator"
Fecha y hora: Lunes 29 de noviembre de 2017, 11:30
Lugar de encuentro: Seminario 2ª planta, IEMath-GR
Resumen: In $\mathbb{R}^n$ ($n$ at most 7), the famous Bernstein's theorem states that every entire solution to the minimal graph equation must be affine. Moreover, entire positive solutions in $\mathbb{R}^n$ are constant in every dimension by a result due to Bombieri, De Giorgi and Miranda. If the underlying space is changed from $\mathbb{R}^n$ to a negatively curved Riemannian manifold, the situation is completely different. Namely, if the sectional curvature of $M$ satisfies suitable bounds, then $M$ possess a wealth of solutions. One way to study the existence of entire, continuous, bounded and non-constant solutions, is to solve the asymptotic Dirichlet problem on Cartan-Hadamard manifolds. In this talk I will discuss about recent existence results for minimal graphs and $f$-minimal graphs. The talk is based on joint works with Jean-Baptiste Casteras and Ilkka Holopainen.