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Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces (Paperback, Softcover reprint of the original 1st ed. 1950)
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Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces (Paperback, Softcover reprint of the original 1st ed. 1950)
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It has always been a temptation for mathematicians to present the
crystallized product of their thoughts as a deductive general
theory and to relegate the individual mathematical phenomenon into
the role of an example. The reader who submits to the dogmatic form
will be easily indoctrinated. Enlightenment, however, must come
from an understanding of motives; live mathematical development
springs from specific natural problems which can be easily
understood, but whose solutions are difficult and demand new
methods of more general significance. The present book deals with
subjects of this category. It is written in a style which, as the
author hopes, expresses adequately the balance and tension between
the individuality of mathematical objects and the generality of
mathematical methods. The author has been interested in Dirichlet's
Principle and its various applications since his days as a student
under David Hilbert. Plans for writing a book on these topics were
revived when Jesse Douglas' work suggested to him a close
connection between Dirichlet's Principle and basic problems
concerning minimal sur faces. But war work and other duties
intervened; even now, after much delay, the book appears in a much
less polished and complete form than the author would have liked."
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