Abstract
We study the properties of the inner radius of multiply connected domains. This conformally invariant quantity coincides with the conformal radius in the simply connected case. Using the vector field method, we prove that the number of critical points of the inner radius is not less than the connectivity order of the domain. The classification of critical points according to their indices is given. We also prove that these points can only be maxima, saddles or semi-saddles.
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This paper has been supported by the Kazan Federal University Strategic Academic Leadership Program (‘‘PRIORITY-2030’’).
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(Submitted by A. M. Elizarov)
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Kazantsev, A.V., Kinder, M.I. On the Inner Radius for Multiply Connected Domains. Lobachevskii J Math 43, 2168–2175 (2022). https://doi.org/10.1134/S1995080222110154
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DOI: https://doi.org/10.1134/S1995080222110154