000 03438nam a22003975i 4500
001 301861
003 MX-SnUAN
005 20170705134255.0
007 cr nn 008mamaa
008 150903s2010 gw | o |||| 0|eng d
020 _a9783642117008
_99783642117008
024 7 _a10.1007/9783642117008
_2doi
035 _avtls000354708
039 9 _a201509030514
_bVLOAD
_c201405060339
_dVLOAD
_y201402191024
_zstaff
040 _aMX-SnUAN
_bspa
_cMX-SnUAN
_erda
050 4 _aQA315-316
100 1 _aDierkes, Ulrich.
_eautor
_9339892
245 1 0 _aRegularity of Minimal Surfaces /
_cby Ulrich Dierkes, Stefan Hildebrandt, Anthony J. Tromba.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2010.
300 _axvii, 623 páginas
_brecurso en línea.
336 _atexto
_btxt
_2rdacontent
337 _acomputadora
_bc
_2rdamedia
338 _arecurso en línea
_bcr
_2rdacarrier
347 _aarchivo de texto
_bPDF
_2rda
490 0 _aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
_x0072-7830 ;
_v340
500 _aSpringer eBooks
505 0 _aBoundary Behaviour of Minimal Surfaces -- Minimal Surfaces with Free Boundaries -- The Boundary Behaviour of Minimal Surfaces -- Singular Boundary Points of Minimal Surfaces -- Geometric Properties of Minimal Surfaces -- Enclosure and Existence Theorems for Minimal Surfaces and H-Surfaces. Isoperimetric Inequalities -- The Thread Problem -- Branch Points.
520 _aRegularity of Minimal Surfaces begins with a survey of minimal surfaces with free boundaries. Following this, the basic results concerning the boundary behaviour of minimal surfaces and H-surfaces with fixed or free boundaries are studied. In particular, the asymptotic expansions at interior and boundary branch points are derived, leading to general Gauss-Bonnet formulas. Furthermore, gradient estimates and asymptotic expansions for minimal surfaces with only piecewise smooth boundaries are obtained. One of the main features of free boundary value problems for minimal surfaces is that, for principal reasons, it is impossible to derive a priori estimates. Therefore regularity proofs for non-minimizers have to be based on indirect reasoning using monotonicity formulas. This is followed by a long chapter discussing geometric properties of minimal and H-surfaces such as enclosure theorems and isoperimetric inequalities, leading to the discussion of obstacle problems and of Plateau´s problem for H-surfaces in a Riemannian manifold. A natural generalization of the isoperimetric problem is the so-called thread problem, dealing with minimal surfaces whose boundary consists of a fixed arc of given length. Existence and regularity of solutions are discussed. The final chapter on branch points presents a new approach to the theorem that area minimizing solutions of Plateau´s problem have no interior branch points.
590 _aPara consulta fuera de la UANL se requiere clave de acceso remoto.
700 1 _aHildebrandt, Stefan.
_eautor
_9339893
700 1 _aTromba, Anthony J.
_eautor
_9160208
710 2 _aSpringerLink (Servicio en línea)
_9299170
776 0 8 _iEdición impresa:
_z9783642116995
856 4 0 _uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-3-642-11700-8
_zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
942 _c14
999 _c301861
_d301861