Certain problems pertaining to differential geometry in the large are treated by function theoretical methods. Theorems of S. Cohn-Vossen (Composition Mathematics 2(1935) 69-133), F. Fiala (Comment. Math. Helv. 13 (1940-41) 293-346) and of Ch. Blanc and F. Fiala (Comment. Math. Helv. 14 (1941-42) 230-233) are proved in new ways and generalized. Results on analytic functions and differentials are implied.
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