000			03899nam a22004935i 4500
003			DE-He213
005			20191014035308.0
007			cr nn 008mamaa
008			130830s2013 gw | s |||| 0|eng d
020	6	4	_a9783642396267 _9978-3-642-39626-7
024	8	7	_a10.1007/978-3-642-39626-7 _2doi
050	8	4	_aQA641-670
072	8	7	_aPBMP _2bicssc
072	8	7	_aMAT012030 _2bisacsh
082			_a516.36 _223
100	8	1	_aLpez, Rafael. _eauthor. _9210453
245	9	7	_aConstant Mean Curvature Surfaces with Boundary _h[electronic resource] / _cby Rafael Lpez.
001			000074482
300	6	4	_aXIV, 292 p. 64 illus. _bonline resource.
490	8	1	_aSpringer Monographs in Mathematics, _x1439-7382
505	8	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	6	4	_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 ǣcompact surfaces with boundaries,ǥ 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	8	0	_aMathematics. _98571
650	8	0	_aDifferential equations, partial. _99614
650	8	0	_aGeometry. _99802
650	8	0	_aGlobal differential geometry. _99530
650			_aMathematics. _98571
650			_aDifferential Geometry. _99532
650			_aPartial Differential Equations. _99616
650			_aGeometry. _99802
710	8	2	_aSpringerLink (Online service) _9210454
773	8	0	_tSpringer eBooks
776			_iPrinted edition: _z9783642396250
830	8	0	_aSpringer Monographs in Mathematics, _x1439-7382 _9210455
856			_uhttp://dx.doi.org/10.1007/978-3-642-39626-7 _zde clik aquí para ver el libro electrónico
264	8	1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2013.
336	6	4	_atext _btxt _2rdacontent
337	6	4	_acomputer _bc _2rdamedia
338	6	4	_aonline resource _bcr _2rdacarrier
347	6	4	_atext file _bPDF _2rda
912	6	4	_aZDB-2-SMA
999			_c74212 _d74212
942			_c05