A Counterexample in the Classification of Open Riemann Surfaces
An HD-function (harmonic and Dirichlet-finite) Ï‰ on a Riemann surface R is called HD-minimal if $\omega > 0$ and every HD-function Ï‰' with 0 â‰¤ Ï‰' â‰¤ Ï‰ reduces to a constant multiple of Ï‰. An HDâˆ¼-function is the limit of a decreasing sequence of positive HD-functions and HDâˆ¼-minimality is defined as in HD-functions. The purpose of the present note is to answer in the affirmative the open question: Does there exist a Riemann surface which carries an HDâˆ¼-minimal function but no HD-minimal functions?
Proceedings of the American Mathematical Society
Kwon, Young Koan.
A Counterexample in the Classification of Open Riemann Surfaces. (1974). Proceedings of the American Mathematical Society. 42, (2), 583-587. Research Collection School Of Accountancy.
Available at: http://ink.library.smu.edu.sg/soa_research/668