Abstract
We construct a boundary integral formula for harmonic functions on smoothly-bordered subdomains of Riemann surfaces embeddable into \({\mathbb {C}}{\mathbb {P}}^2\). The formula may be considered as an analogue of the Green’s formula for domains in \({\mathbb {C}}\).
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29 September 2021
A Correction to this paper has been published: https://doi.org/10.1007/s40315-021-00418-0
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Acknowledgements
The author would like to thank Dima Khavinson for reading the manuscript and for bringing the author’s attention to articles [10,11,12], where the problem of multivaluedness of holomorphic functions with fixed real part on multiply connected domains and on Riemann surfaces was addressed. The author also would like to thank the referee for suggestions improving the exposition of results.
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Communicated by Norman Levenberg.
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Polyakov, P.L. Boundary Integral Formula for Harmonic Functions on Riemann Surfaces. Comput. Methods Funct. Theory 20, 235–253 (2020). https://doi.org/10.1007/s40315-020-00308-x
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DOI: https://doi.org/10.1007/s40315-020-00308-x