H. E. Rauch, Function Theorist
H. E. Rauch made important contributions to the theory of closed Riemann surfaces throughout his mathematical career. For example his 1954 papers  and  with M. Gerstenhaber propose a forward-looking method for using the then undeveloped theory of harmonic maps to prove Teichmüller’s theorem about extremal quasi-conformal maps. His 1979 paper  with L. Keen and A. T. Vasquez sheds interesting light on the accessory parameter problem in the uniformization of punctured tori. His work thus covers far too much ground to be surveyed in one article, but his books and papers reveal a striking consistency of purpose and point of view. They deal with central questions and they show his knowledge of the classical literature and his love of concrete examples and explicit computation, traits that he successfully transmitted to his graduate students.
Unable to display preview. Download preview PDF.
- Ahlfors, L. V.: The complex analytic structure of the space of closed Riemann surfaces. In: Analytic Functions (R. Nevanlinna et al. eds.), pp. 45–66. Princeton University Press, Princeton, N.J. 1960Google Scholar
- Bers, L.: Spaces of Riemann surfaces. In: Proceedings of the International Congress of Mathematicians (Edinburgh, 1958), pp. 349–361. Cambridge University Press, N.Y. 1960Google Scholar
- Hamilton, R. S.: Variation of structure on Riemann surfaces. Princeton University thesis, 1966Google Scholar
- Rauch, H. E.; Lewittes, J.: The Riemann surface of Klein with 168 automorphisms. In: Problems in Analysis, a symposium in honor of Solomon Bochner, pp. 297–308. Princeton University Press, Princeton, N.J. 1970Google Scholar
- Tretkoff, C. L.; Tretkoff, M. D.: Combinatorial group theory. Riemann surfaces, and differential equations. Adv. in Math, (to appear)Google Scholar