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Teichmuller Theory in Riemannian Geometry (Paperback, 1992 ed.)
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Teichmuller Theory in Riemannian Geometry (Paperback, 1992 ed.)
Series: Lectures in Mathematics. ETH Zurich
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These lecture notes are based on the joint work of the author and
Arthur Fischer on Teichmiiller theory undertaken in the years
1980-1986. Since then many of our colleagues have encouraged us to
publish our approach to the subject in a concise format, easily
accessible to a broad mathematical audience. However, it was the
invitation by the faculty of the ETH Ziirich to deliver the ETH N
achdiplom-Vorlesungen on this material which provided the
opportunity for the author to develop our research papers into a
format suitable for mathematicians with a modest background in
differential geometry. We also hoped it would provide the basis for
a graduate course stressing the application of fundamental ideas in
geometry. For this opportunity the author wishes to thank Eduard
Zehnder and Jiirgen Moser, acting director and director of the
Forschungsinstitut fiir Mathematik at the ETH, Gisbert Wiistholz,
responsible for the Nachdiplom Vorlesungen and the entire ETH
faculty for their support and warm hospitality. This new approach
to Teichmiiller theory presented here was undertaken for two
reasons. First, it was clear that the classical approach, using the
theory of extremal quasi-conformal mappings (in this approach we
completely avoid the use of quasi-conformal maps) was not easily
applicable to the theory of minimal surfaces, a field of interest
of the author over many years. Second, many other active
mathematicians, who at various times needed some Teichmiiller
theory, have found the classical approach inaccessible to them.
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