Year: 2025
Type: preprint
Abstract: We consider the extension to higher genus Riemann surfaces of the classical Chebotarev problem, with a view towards the development of the theory of Padé\ approximants on algebraic curves. To this end we define an appropriate notion of capacity that mimics the standard one, following works of Chirka and of the author and collaborators. The nontrivial topology of the Riemann surface requires further specification of the ``homotopy class'' of the continua in the solution of the Chebotarev problem. We also discuss the relationship of this problem to the theory of Jenkins-Strebel quadratic differentials.
Source: arXiv (Cornell University)
Author: Bertola, Marco
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6948520387
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