POTENTIAL THEORY OF BIHARMONIC FUNCTIONS ON RIEMANN SURFACES
Abstract
This note develops a potential theory of biharmonic functions defined on parabolic or hyperbolic Riemann surfaces. The novel feature is that the proofs do not make explicit use of derivatives of functions on the surfaces. A classification theory of Riemann surfaces based on the properties of biharmonic functions and bipotentials is introduced.
Fields of Study & Subjects
Algebraic and Geometric Analysis
Analytic and geometric function theory
Holomorphic and Operator Theory
Publication details
- Journal / source
- Far East Journal of Mathematical Sciences (FJMS)
- Volume
- 143
- Issue
- 2
- Pages
- 549–561
- Publication date
- 3 January 2026