# Meromorphic differentials with twisted coefficients on compact Riemann surfaces

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Let Î± be an entire function, $a_{n-1},\ldots,a_{1},a_{0}$, R be small functions of f, and let $n\geq2$ be an integer. Then, for any positive integer k, the differential equation $f^{n}f^{(k)}+a_{n-1}f^{n-1}+\cdots+a_{1}f+a_{0}=R\mathrm{e}^{\alpha}$ has transcendental meromorphic solutions...

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There are many articles in the literature dealing with the first-order and the second-order differential subordination and superordination problems for analytic functions in the unit disk, but only a few articles are dealing with the above problems in the third-order case (see, e.g., Antonino...

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Deformations of Dubrovin's Hurwitz Frobenius manifolds are constructed. The deformations depend on g(g+1)/2 complex parameters, where g is the genus of the corresponding Riemann surface. In genus one the flat metric of the deformed Frobenius manifold coincides with a metric associated to the...