Local maxima of the spherical derivative

Kodai Mathematical Journal

Shinji Yamashita¹ 

[1] DEPARTMENT OF MATHEMATICS TOKYO METROPOLITAN UNIVERSITY

关键词: Spherical derivative of a meromorphic function;    Schwarzian derivative;    PDF with nonlinear term;   

DOI  :  10.2996/kmj/1138039391

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(12)Let a function f be nonconstant and meromorphic in a domain D in the plane, and let M(f) be the set of points where the spherical derivative |f'|/(1+|f|2) has local maxima. The components of M(f) are at most countable and each component is (i) an isolated point, (ii) a noncompact simple analytic arc terminating nowhere in D, or, (iii) an analytic Jordan curve. Tangents to a component of type (ii) or (iii) are expressed by the argument of the Schwarzian derivative of f. If Δ is the Jordan domain bounded by a component of type (iii) and if Δ⊂D, then the spherical area of the Riemann surface f(Δ) can be expressed by the total number of the zeros and poles of f' in Δ. Solutions of a nonlinear partial differential equation will be considered in connection with the spherical derivative.

【 授权许可】

Unknown