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H. E. Rauch, Function Theorist

In: Differential Geometry and Complex Analysis

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  • Clifford J. Earle

Abstract

H. E. Rauch made important contributions to the theory of closed Riemann surfaces throughout his mathematical career. For example his 1954 papers [9] and [10] 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 [14] 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.

Suggested Citation

  • Clifford J. Earle, 1985. "H. E. Rauch, Function Theorist," Springer Books, in: Isaac Chavel & Hershel M. Farkas (ed.), Differential Geometry and Complex Analysis, pages 15-31, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-69828-6_2
    DOI: 10.1007/978-3-642-69828-6_2
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