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Determination of period matrix of double of surface with boundary via its DN map

Part of: Miscellaneous topics - Partial differential equations Riemann surfaces Commutative Banach algebras and commutative topological algebras

Published online by Cambridge University Press:  07 April 2025

Dmitrii Korikov Open the ORCID record for Dmitrii Korikov [Opens in a new window]
Dmitrii Korikov*
Affiliation:
St.Petersburg Department of Steklov Mathematical Institute, Saint Petersburg, Russia
*
e-mail: dmitrii.v.korikov@gmail.com
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Abstract

As is well-known, the conformal class of a surface M with boundary is determined by its Diriclet-to-Neumann (DN) map $\Lambda $. We propose an algorithm for determination of the b-period matrix $\mathbb {B}$ of the (Schottky) double of M via $\Lambda $.

Keywords

Electric impedance tomography of surfacesb-period matrixDirichlet-to-Neumann mapstability of determinationmoduli space

MSC classification

Primary: 35R30: Inverse problems 46J15: Banach algebras of differentiable or analytic functions, $H^p$-spaces 46J20: Ideals, maximal ideals, boundaries 30F15: Harmonic functions on Riemann surfaces

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Type
Article
Information
Canadian Journal of Mathematics , First View , pp. 1 - 24
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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