000 03066nam a22004457a 4500
001 sulb-eb0026167
003 BD-SySUS
005 20160413122614.0
007 cr nn 008mamaa
008 140513s2013 it | s |||| 0|eng d
020 _a9788876424298
_9978-88-7642-429-8
024 7 _a10.1007/978-88-7642-429-8
_2doi
050 4 _aQA440-699
072 7 _aPBM
_2bicssc
072 7 _aMAT012000
_2bisacsh
082 0 4 _a516
_223
100 1 _aBellettini, Giovanni.
_eauthor.
245 1 0 _aLecture Notes on Mean Curvature Flow, Barriers and Singular Perturbations
_h[electronic resource] /
_cby Giovanni Bellettini.
264 1 _aPisa :
_bScuola Normale Superiore :
_bImprint: Edizioni della Normale,
_c2013.
300 _aApprox. 350 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aPublications of the Scuola Normale Superiore ;
_v12
505 0 _aSigned distance from a smooth boundary -- Mean curvature vector and second fundamental form -- First variations of volume integrals and of the perimeter -- Smooth mean curvature flows -- Huisken’s monotonicity formula -- Inclusion principle. Local well posedness: the approach of Evans–Spruck -- Grayson’s example -- De Giorgi’s barriers -- Inner and outer regularizations -- An example of fattening -- Ilmanen’s interposition lemma -- The avoidance principle -- Comparison between barriers and a generalized evolution -- Barriers and level set evolution -- Parabolic singular perturbations: formal matched asymptotics, convergence and error estimate.
520 _aThe aim of the book is to study some aspects of geometric evolutions, such as mean curvature flow and anisotropic mean curvature flow of hypersurfaces. We analyze the origin of such flows and their geometric and variational nature. Some of the most important aspects of mean curvature flow are described, such as the comparison principle and its use in the definition of suitable weak solutions. The anisotropic evolutions, which can be considered as a generalization of mean curvature flow, are studied from the view point of Finsler geometry. Concerning singular perturbations, we discuss the convergence of the Allen–Cahn (or Ginsburg–Landau) type equations to (possibly anisotropic) mean curvature flow before the onset of singularities in the limit problem. We study such kinds of asymptotic problems also in the static case, showing convergence to prescribed curvature-type problems.
650 0 _aMathematics.
650 0 _aGeometry.
650 1 4 _aMathematics.
650 2 4 _aGeometry.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9788876424281
830 0 _aPublications of the Scuola Normale Superiore ;
_v12
856 4 0 _uhttp://dx.doi.org/10.1007/978-88-7642-429-8
912 _aZDB-2-SMA
942 _2Dewey Decimal Classification
_ceBooks
999 _c48259
_d48259