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math.NA2024
Computation of harmonic functions on higher genus surfaces
Mickaël Nahon, Édouard Oudet
We extend a classical approximation result of harmonic functions in planar domains due to Bernstein and Walsch to the setting of harmonic functions in Riemann surfaces. This result…
math.NA2023
Harmonic functions on finitely-connected tori
Chiu-Yen Kao, Braxton Osting, Édouard Oudet
In this paper, we prove a Logarithmic Conjugation Theorem on finitely-connected tori. The theorem states that a harmonic function can be written as the real part of a function whos…