ⅠMore than fifty years ago, Henri Cartant ~j suggested that geometric function theory ofone complex variable should be extended to biholomorphic mappings of several complexvariables. In particular, he cited the speci...ⅠMore than fifty years ago, Henri Cartant ~j suggested that geometric function theory ofone complex variable should be extended to biholomorphic mappings of several complexvariables. In particular, he cited the special classes of starlike and convex mappings asappropriate topics for generalization. In noting some of the difficulties of generalization, hepointed out the Growth Theorem as one of the results that would not extend to thepolydisc (nor to the ball). Also, he observed that for normalized biholomorphic展开更多
文摘ⅠMore than fifty years ago, Henri Cartant ~j suggested that geometric function theory ofone complex variable should be extended to biholomorphic mappings of several complexvariables. In particular, he cited the special classes of starlike and convex mappings asappropriate topics for generalization. In noting some of the difficulties of generalization, hepointed out the Growth Theorem as one of the results that would not extend to thepolydisc (nor to the ball). Also, he observed that for normalized biholomorphic
文摘ⅠThe classical distortion theorems for families of univalent functions have been studied not later than 1907 when Kbe discovered his 'Verzerrangsatz'.
