Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 51, Number 1 (1999), 167-179.
Boundary behavior of positive solutions of on a Riemann surface
The classical Fatou limit theorem was extended to the case of positive harmonic functions on a hyperbolic Riemann surface 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 whose complements are closed and thin at a minimal boundary point of . We shall consider such a problem for positive solutions of the Schrödinger equation on a hyperbolic Riemann surface.
J. Math. Soc. Japan, Volume 51, Number 1 (1999), 167-179.
First available in Project Euclid: 10 June 2008
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Primary: 31A35: Connections with differential equations
SATŌ, Takeyoshi. Boundary behavior of positive solutions of $\Delta u=Pu$ on a Riemann surface. J. Math. Soc. Japan 51 (1999), no. 1, 167--179. doi:10.2969/jmsj/05110167. https://projecteuclid.org/euclid.jmsj/1213108356