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Seminars

Existence of integrable harmonic functions on a complete Riemannian manifold

Hold Date
2017-10-20 16:00〜2017-10-20 17:30
Place
Seminar Room W1-D-725, West Zone 1, Ito campus, Kyushu University
Object person
 
Speaker
Jun MASAMUNE (Hokkaido University)

Abstract:
The celebrated Yau’s $L^p$-Liouville theorem says that a complete Riemannian manifold does not admit any non-trivial $L^p$ harmonic function for $p>1$. In general, the case of $p=2$ is related with the essential self-adjointness of the Laplacian, and hence, we observe the $L^2$-Liouville property fails for certain incomplete manifolds. For the case p=1, the situation drastically changes even for complete manifolds, and in this talk, inspired by the observation above, we will learn how to construct integrable harmonic functions under certain potential analytical conditions of the manifold.

Based on a joint work with A. Grigoryan and M. Murata.