000			05034nam a22005895i 4500
003			DE-He213
005			20191014004541.0
007			cr nn 008mamaa
008			100825s2010 gw | s |||| 0|eng d
020	6	4	_a9783642116988 _9978-3-642-11698-8
024	8	7	_a10.1007/978-3-642-11698-8 _2doi
050	8	4	_aQA315-316
050	8	4	_aQA402.3
050	8	4	_aQA402.5-QA402.6
072	8	7	_aPBKQ _2bicssc
072	8	7	_aPBU _2bicssc
072	8	7	_aMAT005000 _2bisacsh
072	8	7	_aMAT029020 _2bisacsh
082			_a515.64 _223
100	8	1	_aDierkes, Ulrich. _eauthor. _9160790
245	9	7	_aMinimal Surfaces _h[electronic resource] / _cby Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny.
001			000067784
300	6	4	_aXVI, 692 p. _bonline resource.
490	8	1	_aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, _x0072-7830 ; _v339
505	8	0	_ato the Geometry of Surfaces and to Minimal Surfaces -- Differential Geometry of Surfaces inThree-Dimensional Euclidean Space -- Minimal Surfaces -- Representation Formulas and Examples ofMinimal Surfaces -- Plateau's Problem -- The Plateau Problem andthePartially Free Boundary Problem -- Stable Minimal- and H-Surfaces -- Unstable Minimal Surfaces -- Graphs with Prescribed Mean Curvature -- to the Douglas Problem -- Problems.
520	6	4	_aMinimal 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 nonconstant harmonic mapping X: \Omega\to\R 3 which is conformally parametrized on \Omega\subset\R 2 and may have branch points. Thereafter the classical theory of minimal surfaces is surveyed, comprising many examples, a treatment of Bjȵrlingós 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 Plateauós 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 Nitscheós uniqueness theorem and Tomiós finiteness result. In addition, a theory of unstable solutions of Plateauós problems is developed which is based on Courantós mountain pass lemma. Furthermore, Dirichletós problem for nonparametric H-surfaces is solved, using the solution of Plateauós problem for H-surfaces and the pertinent estimates.
650	8	0	_aMathematics. _98571
650	8	0	_aFunctions of complex variables. _911422
650	8	0	_aDifferential equations, partial. _99614
650	8	0	_aGlobal differential geometry. _99530
650			_aMathematics. _98571
650			_aCalculus of Variations and Optimal Control, Optimization. _911366
650			_aDifferential Geometry. _99532
650			_aPartial Differential Equations. _99616
650			_aFunctions of a Complex Variable. _911424
650			_aTheoretical, Mathematical and Computational Physics. _921503
700	8	1	_aHildebrandt, Stefan. _eauthor. _9160791
700	8	1	_aSauvigny, Friedrich. _eauthor. _9160792
710	8	2	_aSpringerLink (Online service) _9160793
773	8	0	_tSpringer eBooks
776			_iPrinted edition: _z9783642116971
830	8	0	_aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, _x0072-7830 ; _v339 _9160794
856			_uhttp://dx.doi.org/10.1007/978-3-642-11698-8 _zde clik aquí para ver el libro electrónico
264	8	1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2010.
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
516	6	4	_aZDB-2-SMA
999			_c67513 _d67513
942			_c05