FIC-UAI Publication Database -- Query Results

Chuaqui, M., & Hernandez, R. (2023). Families of homomorphic mappings in the polydisk. Complex Var. Elliptic. Equ., Early Access. Abstract: We study classes of locally biholomorphic mappings defined in the polydisk P-n that have bounded Schwarzian operator in the Bergman metric. We establish important properties of specific solutions of the associated system of differential equations, and show a geometric connection between the order of the classes and a covering property. We show for modified and slightly larger classes that the order is Lipschitz continuous with respect to the bound on the Schwarzian, and use this to estimate the order of the original classes. Keywords: Schwarzian operator; polydiskl; ocally biholomorphic; norm; covering show.php?record=1841
Efraimidis, I., Gaona, J., Hernandez, R., & Venegas, O. (2017). On harmonic Bloch-type mappings. Complex Var. Elliptic Equ., 62(8), 1081–1092. Abstract: Let f be a complex-valued harmonicmapping defined in the unit disk D. We introduce the following notion: we say that f is a Bloch-type function if its Jacobian satisfies This gives rise to a new class of functions which generalizes and contains the well-known analytic Bloch space. We give estimates for the schlicht radius, the growth and the coefficients of functions in this class. We establish an analogue of the theorem which, roughly speaking, states that for. analytic log. is Bloch if and only if. is univalent. Keywords: Bloch functions; harmonic functions; Jacobian; univalent functions; schlicht radius; growth estimates; coefficient estimates; 30C25; 30C50; 30D45; 30H30 show.php?record=729

Abstract: We study classes of locally biholomorphic mappings defined in the polydisk P-n that have bounded Schwarzian operator in the Bergman metric. We establish important properties of specific solutions of the associated system of differential equations, and show a geometric connection between the order of the classes and a covering property. We show for modified and slightly larger classes that the order is Lipschitz continuous with respect to the bound on the Schwarzian, and use this to estimate the order of the original classes.

Abstract: Let f be a complex-valued harmonicmapping defined in the unit disk D. We introduce the following notion: we say that f is a Bloch-type function if its Jacobian satisfies This gives rise to a new class of functions which generalizes and contains the well-known analytic Bloch space. We give estimates for the schlicht radius, the growth and the coefficients of functions in this class. We establish an analogue of the theorem which, roughly speaking, states that for. analytic log. is Bloch if and only if. is univalent.

Keywords: Bloch functions; harmonic functions; Jacobian; univalent functions; schlicht radius; growth estimates; coefficient estimates; 30C25; 30C50; 30D45; 30H30

show.php?record=729