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001 | 301861 | ||
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007 | cr nn 008mamaa | ||
008 | 150903s2010 gw | o |||| 0|eng d | ||
020 |
_a9783642117008 _99783642117008 |
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024 | 7 |
_a10.1007/9783642117008 _2doi |
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035 | _avtls000354708 | ||
039 | 9 |
_a201509030514 _bVLOAD _c201405060339 _dVLOAD _y201402191024 _zstaff |
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_aMX-SnUAN _bspa _cMX-SnUAN _erda |
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050 | 4 | _aQA315-316 | |
100 | 1 |
_aDierkes, Ulrich. _eautor _9339892 |
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245 | 1 | 0 |
_aRegularity of Minimal Surfaces / _cby Ulrich Dierkes, Stefan Hildebrandt, Anthony J. Tromba. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2010. |
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300 |
_axvii, 623 páginas _brecurso en línea. |
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336 |
_atexto _btxt _2rdacontent |
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_acomputadora _bc _2rdamedia |
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_arecurso en línea _bcr _2rdacarrier |
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_aarchivo de texto _bPDF _2rda |
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490 | 0 |
_aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, _x0072-7830 ; _v340 |
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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 |
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700 | 1 |
_aTromba, Anthony J. _eautor _9160208 |
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710 | 2 |
_aSpringerLink (Servicio en línea) _9299170 |
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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) |
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_c301861 _d301861 |