By Anthony Tromba
Those lecture notes are in keeping with the joint paintings of the writer and Arthur Fischer on Teichmiiller thought undertaken within the years 1980-1986. considering then a lot of our colleagues have inspired us to submit our method of the topic in a concise structure, simply available to a large mathematical viewers. even if, it used to be the invitation by means of the school of the ETH Ziirich to carry the ETH N achdiplom-Vorlesungen in this fabric which supplied the chance for the writer to improve our study papers right into a structure appropriate for mathematicians with a modest heritage in differential geometry. We additionally was hoping it should give you the foundation for a graduate path stressing the applying of primary rules in geometry. For this chance the writer needs to thank Eduard Zehnder and Jiirgen Moser, appearing director and director of the Forschungsinstitut fiir Mathematik on the ETH, Gisbert Wiistholz, accountable for the Nachdiplom Vorlesungen and the whole ETH school for his or her help and hot hospitality. This new method of Teichmiiller concept awarded right here used to be undertaken for 2 purposes. First, it was once transparent that the classical method, utilizing the speculation of extremal quasi-conformal mappings (in this strategy we thoroughly stay away from using quasi-conformal maps) used to be no longer simply appropriate to the speculation of minimum surfaces, a box of curiosity of the writer over decades. moment, many different energetic mathematicians, who at a variety of instances wanted a few Teichmiiller idea, have came across the classical strategy inaccessible to them.
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