000			03226nam a22004695i 4500
001			978-3-0346-0213-6
003			DE-He213
005			20140220084518.0
007			cr nn 008mamaa
008			100301s2010 sz | s |||| 0|eng d
020			_a9783034602136 _9978-3-0346-0213-6
024	7		_a10.1007/978-3-0346-0213-6 _2doi
050		4	_aQA641-670
072		7	_aPBMP _2bicssc
072		7	_aMAT012030 _2bisacsh
082	0	4	_a516.36 _223
100	1		_aRitoré, Manuel. _eauthor.
245	1	0	_aMean Curvature Flow and Isoperimetric Inequalities _h[electronic resource] / _cby Manuel Ritoré, Carlo Sinestrari.
264		1	_aBasel : _bBirkhäuser Basel, _c2010.
300			_bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aAdvanced Courses in Mathematics — CRM Barcelona, Centre de Recerca Matemàtica
505	0		_aFormation of Singularities in the Mean Curvature Flow -- Geometry of hypersurfaces -- Examples -- Local existence and formation of singularities -- Invariance properties -- Singular behaviour of convex surfaces -- Convexity estimates -- Rescaling near a singularity -- Huisken’s monotonicity formula -- Cylindrical and gradient estimates -- Mean curvature flow with surgeries -- Geometric Flows, Isoperimetric Inequalities and Hyperbolic Geometry -- The classical isoperimetric inequality in Euclidean space -- Surfaces -- Higher dimensions -- Some applications to hyperbolic geometry.
520			_aGeometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface evolution in certain physical models. This is related to the property that such a flow is the gradient flow of the area functional and therefore appears naturally in problems where a surface energy is minimized. The mean curvature flow also has many geometric applications, in analogy with the Ricci flow of metrics on abstract riemannian manifolds. One can use this flow as a tool to obtain classification results for surfaces satisfying certain curvature conditions, as well as to construct minimal surfaces. Geometric flows, obtained from solutions of geometric parabolic equations, can be considered as an alternative tool to prove isoperimetric inequalities. On the other hand, isoperimetric inequalities can help in treating several aspects of convergence of these flows. Isoperimetric inequalities have many applications in other fields of geometry, like hyperbolic manifolds.
650		0	_aMathematics.
650		0	_aGlobal analysis.
650		0	_aGlobal differential geometry.
650	1	4	_aMathematics.
650	2	4	_aDifferential Geometry.
650	2	4	_aGlobal Analysis and Analysis on Manifolds.
700	1		_aSinestrari, Carlo. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783034602129
830		0	_aAdvanced Courses in Mathematics — CRM Barcelona, Centre de Recerca Matemàtica
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-0346-0213-6
912			_aZDB-2-SMA
999			_c111099 _d111099