Boundary behavior of positive solutions of Δu=Pu on a Riemann surface
Takeyoshi SATŌ · Journal of the Mathematical Society of Japan · 1999
The classical Fatou limit theorem was extended to the case of positive harmonic functions on a hyperbolic Riemann surface R by Constantinescu-Cornea. They used extensively the notions of Martin's boundary and fine limit following the filter generated by the base of the subsets of R whose complements are closed and thin at a minimal boundary point of R. We shall consider such a problem for positive solutions of the Schrödinger equation on a hyperbolic Riemann surface.