000			03442nam a22005175i 4500
003			DE-He213
005			20191014015755.0
007			cr nn 008mamaa
008			120104s2012 gw | s |||| 0|eng d
020	6	4	_a9783642256202 _9978-3-642-25620-2
024	8	7	_a10.1007/978-3-642-25620-2 _2doi
050	8	4	_aQA331-355
072	8	7	_aPBKD _2bicssc
072	8	7	_aMAT034000 _2bisacsh
082			_a515.9 _223
100	8	1	_aTromba, Anthony. _eauthor. _9187348
245	9	9	_aA Theory of Branched Minimal Surfaces _h[electronic resource] / _cby Anthony Tromba.
001			000071311
300	6	4	_aX, 194 p. _bonline resource.
490	8	1	_aSpringer Monographs in Mathematics, _x1439-7382
505	8	0	_a1.Introduction -- 2.Higher order Derivatives of Dirichlets' Energy -- 3.Very Special Case; The Theorem for n + 1 Even and m + 1 Odd -- 4.The First Main Theorem; Non-Exceptional Branch Points -- 5.The Second Main Theorem: Exceptional Branch Points; The Condition k > l -- 6.Exceptional Branch Points Without The Condition k > l -- 7.New Brief Proofs of the Gulliver-Osserman-Royden Theorem -- 8.Boundary Branch Points -- Scholia -- Appendix -- Bibliography.
520	6	4	_aOne of the most elementary questions in mathematics is whether an area minimizing surface spanning a contour in three space is immersed or not; i.e. does its derivative have maximal rank everywhere. The purpose of this monograph is to present an elementary proof of this very fundamental and beautiful mathematical result. The exposition follows the original line of attack initiated by Jesse Douglas in his Fields medal work in 1931, namely use Dirichlet's energy as opposed to area. Remarkably, the author shows how to calculate arbitrarily high orders of derivatives of Dirichlet's energy defined on the infinite dimensional manifold of all surfaces spanning a contour, breaking new ground in the Calculus of Variations, where normally only the second derivative or variation is calculated. The monograph begins with easy examples leading to a proof in a large number of cases that can be presented in a graduate course in either manifolds or complex analysis. Thus this monograph requires only the most basic knowledge of analysis, complex analysis and topology and can therefore be read by almost anyone with a basic graduate education.
650	8	0	_aMathematics. _98571
650	8	0	_aFunctions of complex variables. _911422
650	8	0	_aGlobal analysis. _917903
650	8	0	_aSequences (Mathematics). _914062
650	8	0	_aGlobal differential geometry. _99530
650			_aMathematics. _98571
650			_aFunctions of a Complex Variable. _911424
650			_aSequences, Series, Summability. _914066
650			_aDifferential Geometry. _99532
650			_aGlobal Analysis and Analysis on Manifolds. _917904
710	8	2	_aSpringerLink (Online service) _9187349
773	8	0	_tSpringer eBooks
776			_iPrinted edition: _z9783642256196
830	8	0	_aSpringer Monographs in Mathematics, _x1439-7382 _9187350
856			_uhttp://dx.doi.org/10.1007/978-3-642-25620-2 _zde clik aquí para ver el libro electrónico
264	8	1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2012.
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			_c71041 _d71041
942			_c05