The maximum modulus set of a quasiregular map

نویسندگان

چکیده

We study, for the first time, maximum modulus set of a quasiregular map. It is easy to see that these sets are necessarily closed, and contain at least one point each modulus. Blumenthal showed entire maps either whole plane, or countable union analytic curves. show in case, by way contrast, any closed containing can be attained as These examples all polynomial type. also that, subject an additional constraint, such even transcendental

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ژورنال

عنوان ژورنال: Geometriae Dedicata

سال: 2021

ISSN: ['0046-5755', '1572-9168']

DOI: https://doi.org/10.1007/s10711-021-00613-2