Jun Masamune (Tohoku University)
When every harmonic function belonging to a space $E$ of functions is identically constant, we say that the $E$-Liouville property holds true. There are different types of Liouville property according to the choice of $E$, closely related with the geometry of the underlying space. In this talk, we will learn a recent development of $E$-Liouville properties when the functions in $E$ satisfies certain integrable conditions. The talk is based on a collaborative effort with Radoslaw Wojciechowski (CUNY).