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010   $a3-642-39626-7
024 7 $a10.1007/978-3-642-39626-7
035   $a(OCoLC)857904343
035   $a(MiFhGG)GVRL6WTT
035   $a(EXLCZ)993710000000015877
100   $a20130821d2013      uy             0
101 0 $aeng
135   $aurun|---uuuua
181   $ctxt
182   $cc
183   $acr
200 10$aConstant mean curvature surfaces with boundary /$fRafael Lopez
205   $a1st ed. 2013.
210  1$aHeidelberg, Germany :$cSpringer,$d2013.
215   $a1 online resource (xiv, 292 pages) $cillustrations
225 1 $aSpringer Monographs in Mathematics,$x1439-7382
300   $a"ISSN: 1439-7382."
311   $a3-642-39625-9 
320   $aIncludes bibliographical references and index.
327   $aIntroduction -- Surfaces with Constant Mean Curvature -- Constant Mean Curvature Embedded Surfaces -- The Flux Formula for Constant Mean Curvature Surfaces -- The Area and the Volume of a Constant Mean Curvature Surface -- Constant Mean Curvature Discs with Circular Boundary -- The Dirichlet Problem of the CMC Equation -- The Dirichlet Problem in Unbounded Domains -- Constant Mean Curvature Surfaces in Hyperbolic Space -- The Dirichlet Problem in Hyperbolic Space -- Constant Mean Curvature Surfaces in Lorentz-Minkowski Space -- Appendix: A. The Variation Formula of the Area and the Volume -- B. Open Questions -- References.
330   $aThe study of surfaces with constant mean curvature (CMC) is one of the main topics in classical differential geometry. Moreover, CMC surfaces are important mathematical models for the physics of interfaces in the absence of gravity, where they separate two different media, or for capillary phenomena. Further, as most techniques used in the theory of CMC surfaces not only involve geometric methods but also PDE and complex analysis, the theory is also of great interest for many other mathematical fields.   While minimal surfaces and CMC surfaces in general have already been treated in the literature, the present work is the first to present a comprehensive study of ?compact surfaces with boundaries,? narrowing its focus to a geometric view. Basic issues include the discussion whether the symmetries of the curve inherit to the surface; the possible values of the mean curvature, area and volume; stability; the circular boundary case; and the existence of the Plateau problem in the non-parametric case. The exposition provides an outlook on recent research but also a set of techniques that allows the results to be expanded to other ambient spaces. Throughout the text, numerous illustrations clarify the results and their proofs.   The book is intended for graduate students and researchers in the field of differential geometry and especially theory of surfaces, including geometric analysis and geometric PDEs. It guides readers up to the state-of-the-art of the theory and introduces them to interesting open problems.
410  0$aSpringer monographs in mathematics.
606   $aSurfaces of constant curvature
606   $aCurves, Algebraic
606   $aBoundary value problems
615  0$aSurfaces of constant curvature.
615  0$aCurves, Algebraic.
615  0$aBoundary value problems.
676   $a510
700   $aLópez$b Rafael$4aut$4http://id.loc.gov/vocabulary/relators/aut$01059546
801  0$bMiFhGG
801  1$bMiFhGG
906   $aBOOK
912   $a9910438037103321
996   $aConstant Mean Curvature Surfaces with Boundary$92506834
997   $aUNINA