Celebratio Mathematica — Chern

Complete Bibliography

Works connected to Norman Morse

Filter the Bibliography List

year	title	people

			clear

article S.-S. Chern: “Complex analytic mappings of Riemann surfaces, I,” Am. J. Math. 82 : 2 (April 1960), pp. 323–337. Dedicated to Professor Marston Morse. MR 0115183 Zbl 0103.30104

The geometrical nature of the theory of functions in one complex variable is a well-known fact and has been particularly emphasized by L. Ahlfors [1937]. It is also the most natural viewpoint, beause complex function thoery should be regarded as the first chapter of the theory of complex analytic mappings of complex manifolds and the classical study of value distributions is the study of the “size” of the image of a complex analytic mapping. We give in this paper a treatment, from a purely differential-geometric viewpoint, of complex analytic mappings of a Riemann surface (= one dimensional complex analytic manifold) into a compact Riemann surface. In the case when the first Riemann surface is a compact one with a finite number of points deleted, we derive defect relations which generalize the classical relations of Nevanlinna–Ahlfors. In a subsequent paper we will consider the case when the first Riemann surface is a compact one with a finite number of points and a finite number of disks deleted. The paper is written for differential geometers, so that concepts currently in use in differential geometry are freely used and a minimum of function theory will be required. The explicit models of the Gaussian plane or the unit disk are avoided.

incollection S.-S. Chern: “Minimal surfaces in an Euclidean space of \( N \) dimensions,” pp. 187–198 in Differential and combinatorial topology (A symposium in honor of Marston Morse). Edited by S. S. Cairns. Princeton Mathematical Series 27. Princeton University Press, 1965. MR 0180926 Zbl 0136.16701

Norman Morse	Related
Stewart Scott Cairns	Related