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Constant Mean Curvature Surfaces with Boundary (Paperback, Softcover reprint of the original 1st ed. 2013)
Loot Price: R3,621
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Constant Mean Curvature Surfaces with Boundary (Paperback, Softcover reprint of the original 1st ed. 2013)
Series: Springer Monographs in Mathematics
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Total price: R3,641
Discovery Miles: 36 410
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The study of surfaces with constant mean curvature (CMC) is one of
the main topics in classical differential geometry. Moreover, CMC
surfaces are important mathematical models for the physics of
interfaces in the absence of gravity, where they separate two
different media or for capillary phenomena. Further, as most
techniques used in the theory of CMC surfaces not only involve
geometric methods but also PDE and complex analysis, the theory is
also of great interest for many other mathematical fields. While
minimal surfaces and CMC surfaces in general have already been
treated in the literature, the present work is the first to present
a comprehensive study of "compact surfaces with boundaries,"
narrowing its focus to a geometric view. Basic issues include the
discussion whether the symmetries of the curve inherit to the
surface; the possible values of the mean curvature, area and
volume; stability; the circular boundary case and the existence of
the Plateau problem in the non-parametric case. The exposition
provides an outlook on recent research but also a set of techniques
that allows the results to be expanded to other ambient spaces.
Throughout the text, numerous illustrations clarify the results and
their proofs. The book is intended for graduate students and
researchers in the field of differential geometry and especially
theory of surfaces, including geometric analysis and geometric
PDEs. It guides readers up to the state-of-the-art of the theory
and introduces them to interesting open problems.
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