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POTENTIAL THEORY OF BIHARMONIC FUNCTIONS ON RIEMANN SURFACES
Keywords:
biharmonic functions and bipotentials on Riemann surfaces, biharmonic Green functionsDOI:
https://doi.org/10.17654/0972087126032Abstract
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.
Received: October 24, 2025
Accepted: December 18, 2025
References
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