Málstofa: Sigmundur Guðmundsson – Stærðfræðistofa

Auka málstofa verður þriðjudaginn 4. október 15:00 í stofu 261 í VRII. Fyrirlesari er Sigmundur Guðmundsson, Háskólanum í Lundi, Svíþjóð.
Titill hans er Complex-Valued Harmonic Morphisms and Proper p-Harmonic Functions on Riemannian Symmetric Spaces – The Method of Eigenfamilies

Abstract:
Complex-valued proper $latex p$-harmonic functions $ϕ : (M, g) \to C$ on a Riemannian manifold are solutions to the $2 p$ -th order PDE $τ^{p} (ϕ) = 0$ such that $τ^{p - 1} (ϕ) \neq 0$ . Here $τ$ is the standard Laplace-Beltrami operator on $(M, g)$ . The literature on biharmonic functions is vast, but with only very few exceptions the domains are either surfaces or open subsets of flat Euclidean space. The development of the last few years has changed this significantly. Recently, explicit proper $p$ -harmonic functions have been constructed on all the classical Riemannian symmetric spaces, for any positive $p$ . This has been achieved by employing the so called „method of eigenfamilies“, earlier developed for the construction of explicit complex-valued harmonic morphisms. In this talk we will explain the background and the method in action. We will then describe the situation in more details for the cases when the Riemannian manifold $(M, g)$ is one of the classical real, complex or quaternionic Grassmannians.