Abstract
We address here the question of the bi-Lipschitz local triviality of a complex polynomial function over a complex value. Our main result states that a non constant complex polynomial admits a locally bi-Lipschitz trivial value if and only if it is a polynomial in one complex variable.
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The authors are very grateful to the anonymous referee for helpful remarks and comments. A. Fernandes was partially supported by FUNCAP/CAPES/CNPq grant 304221/2017-1; V. Grandjean was partially supported by FUNCAP/CAPES/CNPq grant 305614/2015-0; C.H. Soares was partially supported by CNPq grant 113058/2016-0.
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Fernandes, A., Grandjean, V. & Soares, H. A note on the local Lipschitz triviality of values of complex polynomial functions. Math. Z. 296, 861–874 (2020). https://doi.org/10.1007/s00209-020-02474-z
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DOI: https://doi.org/10.1007/s00209-020-02474-z