Monday Analysis Seminar: Uniqueness of $L^1$ harmonic functions on rotationally symmetric Riemannian manifolds

2013-5-27 14:45 - 2013-5-27 16:15
Faculty of Science Buliding #3 Room 210
Minoru Murata (Prof. Emer. Tokyo Institute of Technology)
We show that any rotationally symmetric Riemannian manifold has the $L^1$-Liouville property for harmonic functions, i.e., any integrable harmonic unction on it must be identically constant. We also give a characterization of a manifold which carries a non-constant $L^1$ nonnegative subharmonic function.