GAMP seminar by Esko Heinonen (Helsinki) – University of Copenhagen

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GAMP seminar by Esko Heinonen (Helsinki)

GAMP (Geometric Analysis and Mathematical Physics) Seminar.

Speaker: Esko Heinonen (Helsinki).

Title: Asymptotic Dirichlet problems for the mean curvature operator.

Abstract: In 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 R^n are constant in every dimension by a result due to Bombieri, De Giorgi and Miranda. If the underlying space is changed from 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 possesses 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 recent results for minimal graphs and f-minimal graphs. The talk is based on joint works with Jean-Baptiste Casteras and Ilkka Holopainen.