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Minimal Surfaces is the first volume of a three volume treatise on
minimal surfaces (Grundlehren Nr. 339-341). Each volume can be read
and studied independently of the others. The central theme is
boundary value problems for minimal surfaces. The treatise is a
substantially revised and extended version of the monograph Minimal
Surfaces I, II (Grundlehren Nr. 295 & 296). The first volume
begins with an exposition of basic ideas of the theory of surfaces
in three-dimensional Euclidean space, followed by an introduction
of minimal surfaces as stationary points of area, or equivalently,
as surfaces of zero mean curvature. The final definition of a
minimal surface is that of a non-constant harmonic mapping X:
\Omega\to\R DEGREES3 which is conformally parametrized on
\Omega\subset\R DEGREES2 and may have branch points. Thereafter the
classical theory of minimal surfaces is surveyed, comprising many
examples, a treatment of Bjorlings initial value problem,
reflection principles, a formula of the second variation of area,
the theorems of Bernstein, Heinz, Osserman, and Fujimoto. The
second part of this volume begins with a survey of Plateaus problem
and of some of its modifications. One of the main features is a
new, completely elementary proof of the fact that area A and
Dirichlet integral D have the same infimum in the class C(G) of
admissible surfaces spanning a prescribed contour G. This leads to
a new, simplified solution of the simultaneous problem of
minimizing A and D in C(G), as well as to new proofs of the mapping
theorems of Riemann and Korn-Lichtenstein, and to a new solution of
the simultaneous Douglas problem for A and D where G consists of
several closed components. Then basic facts of stable minimal
surfaces are derived; this is done in the context of stable
H-surfaces (i.e. of stable surfaces of prescribed mean curvature
H), especially of cmc-surfaces (H = const), and leads to curvature
estimates for stable, immersed cmc-surfaces and to Nitsches
uniqueness theorem and Tomis finiteness result. In addition, a
theory of unstable solutions of Plateaus problems is developed
which is based on Courants mountain pass lemma. Furthermore,
Dirichlets problem for nonparametric H-surfaces is solved, using
the solution of Plateaus problem for H-surfaces and the pertinent
estimates."
This is a reproduction of a book published before 1923. This book
may have occasional imperfections such as missing or blurred pages,
poor pictures, errant marks, etc. that were either part of the
original artifact, or were introduced by the scanning process. We
believe this work is culturally important, and despite the
imperfections, have elected to bring it back into print as part of
our continuing commitment to the preservation of printed works
worldwide. We appreciate your understanding of the imperfections in
the preservation process, and hope you enjoy this valuable book.
++++ The below data was compiled from various identification fields
in the bibliographic record of this title. This data is provided as
an additional tool in helping to ensure edition identification:
++++ Job: Un Drama Engiadinais Del XVI.secul. Nouvamaing Publicho
with A German Glossary] Da I.Ulrich Jakob Ulrich
This is an EXACT reproduction of a book published before 1923. This
IS NOT an OCR'd book with strange characters, introduced
typographical errors, and jumbled words. This book may have
occasional imperfections such as missing or blurred pages, poor
pictures, errant marks, etc. that were either part of the original
artifact, or were introduced by the scanning process. We believe
this work is culturally important, and despite the imperfections,
have elected to bring it back into print as part of our continuing
commitment to the preservation of printed works worldwide. We
appreciate your understanding of the imperfections in the
preservation process, and hope you enjoy this valuable book.
This is an EXACT reproduction of a book published before 1923. This
IS NOT an OCR'd book with strange characters, introduced
typographical errors, and jumbled words. This book may have
occasional imperfections such as missing or blurred pages, poor
pictures, errant marks, etc. that were either part of the original
artifact, or were introduced by the scanning process. We believe
this work is culturally important, and despite the imperfections,
have elected to bring it back into print as part of our continuing
commitment to the preservation of printed works worldwide. We
appreciate your understanding of the imperfections in the
preservation process, and hope you enjoy this valuable book.
This is a reproduction of a book published before 1923. This book
may have occasional imperfections such as missing or blurred pages,
poor pictures, errant marks, etc. that were either part of the
original artifact, or were introduced by the scanning process. We
believe this work is culturally important, and despite the
imperfections, have elected to bring it back into print as part of
our continuing commitment to the preservation of printed works
worldwide. We appreciate your understanding of the imperfections in
the preservation process, and hope you enjoy this valuable book.
This is a reproduction of a book published before 1923. This book
may have occasional imperfections such as missing or blurred pages,
poor pictures, errant marks, etc. that were either part of the
original artifact, or were introduced by the scanning process. We
believe this work is culturally important, and despite the
imperfections, have elected to bring it back into print as part of
our continuing commitment to the preservation of printed works
worldwide. We appreciate your understanding of the imperfections in
the preservation process, and hope you enjoy this valuable book.
++++ The below data was compiled from various identification fields
in the bibliographic record of this title. This data is provided as
an additional tool in helping to ensure edition identification:
++++ Proben Der Franzosischen Novellistik Des Sechzehnten
Jahrhunderts: Texte Und Kommentar Herausgegeben. I Jakob Ulrich
Renger, 1906
This is a reproduction of a book published before 1923. This book
may have occasional imperfections such as missing or blurred pages,
poor pictures, errant marks, etc. that were either part of the
original artifact, or were introduced by the scanning process. We
believe this work is culturally important, and despite the
imperfections, have elected to bring it back into print as part of
our continuing commitment to the preservation of printed works
worldwide. We appreciate your understanding of the imperfections in
the preservation process, and hope you enjoy this valuable book.
Italienische Bibliothek V2. This Book Is In German.
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