Boundary Integral Formula for Harmonic Functions on Riemann Surfaces

We construct a boundary integral formula for harmonic functions on smoothly-bordered subdomains of Riemann surfaces embeddable into C P 2 . The formula may be considered as an analogue of the Green’s formula for domains in C .

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Bibliographic Details
Published in:Computational methods and function theory 2020-06, Vol.20 (2), p.235-253
Main Author: Polyakov, Peter L.
Format: Article
Language:English
Subjects:
Analysis
Computational Mathematics and Numerical Analysis
Functions of a Complex Variable
Harmonic functions
Integrals
Mathematics
Mathematics and Statistics
Riemann surfaces
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Description
Summary:We construct a boundary integral formula for harmonic functions on smoothly-bordered subdomains of Riemann surfaces embeddable into C P 2 . The formula may be considered as an analogue of the Green’s formula for domains in C .
ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-020-00308-x