Journal of the Mathematical Society of Japan

Boundary behavior of positive solutions of Δu=Pu on a Riemann surface

Takeyoshi SATŌ

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Abstract

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.

Article information

Source
J. Math. Soc. Japan, Volume 51, Number 1 (1999), 167-179.

Dates
First available in Project Euclid: 10 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1213108356

Digital Object Identifier
doi:10.2969/jmsj/05110167

Mathematical Reviews number (MathSciNet)
MR1661016

Zentralblatt MATH identifier
0940.31003

Subjects
Primary: 31A35: Connections with differential equations

Keywords
Fatou limit theorem Schr\"{o}dinger's equation Martin boundary fine limit

Citation

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


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