In this paper,the inner radius of univalency of hyperbolic domains by pre-Schwarzian derivative is studied,and some general formulas for the lower bound of the inner radius are established. As their applications,the l...In this paper,the inner radius of univalency of hyperbolic domains by pre-Schwarzian derivative is studied,and some general formulas for the lower bound of the inner radius are established. As their applications,the lower bounds of inner radiuses for angular domains and strongly starlike domains are obtained.展开更多
In this paper, the authors introduce a definition of the Schwarzian derivative of any locally univalent harmonic mapping defined on a simply connected domain in the complex plane. Using the new definition, the authors...In this paper, the authors introduce a definition of the Schwarzian derivative of any locally univalent harmonic mapping defined on a simply connected domain in the complex plane. Using the new definition, the authors prove that any harmonic mapping f which maps the unit disk onto a convex domain has Schwarzian norm ||Sf||≤ 6. Furthermore, any locally univalent harmonic mapping f which maps the unit disk onto an arbitrary regular n-gon has Schwarzian norm||Sf||≤8/3.展开更多
In this paper,we study univalent functions f for which log f’belongs to the analytic Morrey spaces.By using the characterization of higher order derivatives of functions in analytic Morrey spaces,we establish some ne...In this paper,we study univalent functions f for which log f’belongs to the analytic Morrey spaces.By using the characterization of higher order derivatives of functions in analytic Morrey spaces,we establish some new descriptions for the analytic Morrey domains in terms of two kinds of generalized Schwarzian derivatives.展开更多
Let U be an open subset of the Riemann sphere C. We give sufficient conditions for which a finite type map f : U →C with at most three singular values has a Siegel disk compactly contained in U and whose boundary is ...Let U be an open subset of the Riemann sphere C. We give sufficient conditions for which a finite type map f : U →C with at most three singular values has a Siegel disk compactly contained in U and whose boundary is a quasicircle containing a unique critical point. The main tool is quasiconformal surgery à la Douady-Ghys-Herman-(S′)wia tek. We also give sufficient conditions for which, instead, ? has not compact closure in U. The main tool is the Schwarzian derivative and area inequalities à la Graczyk-(S′)wia tek.展开更多
Using two different Lie groups, two different Schwarzian derivatives of holomorphic mappings on domains in C n are defined and discussed. The necessary and sufficient conditions for annihilation of these two different...Using two different Lie groups, two different Schwarzian derivatives of holomorphic mappings on domains in C n are defined and discussed. The necessary and sufficient conditions for annihilation of these two different Schwarzian derivatives are given.展开更多
In the point view of Lie group, the cross ratio and Schwarzian derivative in C n are defined and discussed, especially the Schwarzian derivative of holomorphic mappings on the domains in matrix space C m×n is def...In the point view of Lie group, the cross ratio and Schwarzian derivative in C n are defined and discussed, especially the Schwarzian derivative of holomorphic mappings on the domains in matrix space C m×n is defined and discussed. It is proved that it is invariant up to similarity under the group of holomorphic automorphism of the Grassmann manifold C G(m,n) . And it is also proved that the Schwarzian derivative equals zero if and only if the mapping is linearly fractional.展开更多
In this paper,some new criteria for univalence of analytic functions defined in the unit disk in terms of two parameters are presented.Moreover,the related result of Aharonov and Elias(Aharonov D,Elias U.Univalence cr...In this paper,some new criteria for univalence of analytic functions defined in the unit disk in terms of two parameters are presented.Moreover,the related result of Aharonov and Elias(Aharonov D,Elias U.Univalence criteria depending on parameters.Anal.Math.Phys.,2014,4(1-2):23–34)is generalized.展开更多
基金This work was partially supported by the National Natural Science Foundation of China(Grant No.10571028).
文摘In this paper,the inner radius of univalency of hyperbolic domains by pre-Schwarzian derivative is studied,and some general formulas for the lower bound of the inner radius are established. As their applications,the lower bounds of inner radiuses for angular domains and strongly starlike domains are obtained.
基金the National Natural Science Foundation of China(No.11261022)。
文摘In this paper, the authors introduce a definition of the Schwarzian derivative of any locally univalent harmonic mapping defined on a simply connected domain in the complex plane. Using the new definition, the authors prove that any harmonic mapping f which maps the unit disk onto a convex domain has Schwarzian norm ||Sf||≤ 6. Furthermore, any locally univalent harmonic mapping f which maps the unit disk onto an arbitrary regular n-gon has Schwarzian norm||Sf||≤8/3.
基金supported by National Natural Science Foundation of China(Grant No.11601100)the PhD research startup foundation of Guizhou Normal University(Grant No.11904-05032130006)supported by National Natural Science Foundation of China(Grant No.11501157)
文摘In this paper,we study univalent functions f for which log f’belongs to the analytic Morrey spaces.By using the characterization of higher order derivatives of functions in analytic Morrey spaces,we establish some new descriptions for the analytic Morrey domains in terms of two kinds of generalized Schwarzian derivatives.
文摘Let U be an open subset of the Riemann sphere C. We give sufficient conditions for which a finite type map f : U →C with at most three singular values has a Siegel disk compactly contained in U and whose boundary is a quasicircle containing a unique critical point. The main tool is quasiconformal surgery à la Douady-Ghys-Herman-(S′)wia tek. We also give sufficient conditions for which, instead, ? has not compact closure in U. The main tool is the Schwarzian derivative and area inequalities à la Graczyk-(S′)wia tek.
文摘Using two different Lie groups, two different Schwarzian derivatives of holomorphic mappings on domains in C n are defined and discussed. The necessary and sufficient conditions for annihilation of these two different Schwarzian derivatives are given.
文摘In the point view of Lie group, the cross ratio and Schwarzian derivative in C n are defined and discussed, especially the Schwarzian derivative of holomorphic mappings on the domains in matrix space C m×n is defined and discussed. It is proved that it is invariant up to similarity under the group of holomorphic automorphism of the Grassmann manifold C G(m,n) . And it is also proved that the Schwarzian derivative equals zero if and only if the mapping is linearly fractional.
基金The NSF(11501001)of Chinathe NSF(1908085MA18)of Anhui Provincethe Foundation(Y01002428)of Anhui University
文摘In this paper,some new criteria for univalence of analytic functions defined in the unit disk in terms of two parameters are presented.Moreover,the related result of Aharonov and Elias(Aharonov D,Elias U.Univalence criteria depending on parameters.Anal.Math.Phys.,2014,4(1-2):23–34)is generalized.
