000 03780nam a22004815i 4500
001 978-3-642-39626-7
003 DE-He213
005 20140220082916.0
007 cr nn 008mamaa
008 130830s2013 gw | s |||| 0|eng d
020 _a9783642396267
_9978-3-642-39626-7
024 7 _a10.1007/978-3-642-39626-7
_2doi
050 4 _aQA641-670
072 7 _aPBMP
_2bicssc
072 7 _aMAT012030
_2bisacsh
082 0 4 _a516.36
_223
100 1 _aLópez, Rafael.
_eauthor.
245 1 0 _aConstant Mean Curvature Surfaces with Boundary
_h[electronic resource] /
_cby Rafael López.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2013.
300 _aXIV, 292 p. 64 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Monographs in Mathematics,
_x1439-7382
505 0 _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.
520 _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.
650 0 _aMathematics.
650 0 _aDifferential equations, partial.
650 0 _aGeometry.
650 0 _aGlobal differential geometry.
650 1 4 _aMathematics.
650 2 4 _aDifferential Geometry.
650 2 4 _aPartial Differential Equations.
650 2 4 _aGeometry.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642396250
830 0 _aSpringer Monographs in Mathematics,
_x1439-7382
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-39626-7
912 _aZDB-2-SMA
999 _c98484
_d98484