LEADER 01069nam a2200313 i 4500 001 991000734899707536 005 20020507172920.0 008 950316s1981 us ||| | eng 020 $a0470273038 035 $ab1075006x-39ule_inst 035 $aLE01301501$9ExL 040 $aDip.to Matematica$beng 082 0 $a514.74 084 $aAMS 58C28 084 $aAMS 58E05 084 $aQA614.58.C37 100 1 $aSinha, D. K.$0534848 245 10$aCatastrophe theory and applications /$cedited by D. K. Sinha 260 $aNew York :$bJ. Wiley & Sons,$cc1981 300 $axi, 158 p. :$bill. ;$c22 cm. 490 0 $aMathematics of mathematical sciences 500 $aBibliography: p. [132]-154. 500 $aIncludes indexes 907 $a.b1075006x$b23-02-17$c28-06-02 912 $a991000734899707536 945 $aLE013 58C SIN11 (1981)$g1$i2013000043760$lle013$o-$pE0.00$q-$rl$s- $t0$u1$v0$w1$x0$y.i10842937$z28-06-02 996 $aCatastrophe theory and applications$9911561 997 $aUNISALENTO 998 $ale013$b01-01-95$cm$da $e-$feng$gus $h0$i1 LEADER 03928nam 22005655 450 001 9910350246903321 005 20200705175138.0 010 $a981-13-7075-3 024 7 $a10.1007/978-981-13-7075-5 035 $a(CKB)4100000008525904 035 $a(DE-He213)978-981-13-7075-5 035 $a(MiAaPQ)EBC5755036 035 $a(PPN)235669490 035 $a(EXLCZ)994100000008525904 100 $a20190409d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aBrakke's Mean Curvature Flow $eAn Introduction /$fby Yoshihiro Tonegawa 205 $a1st ed. 2019. 210 1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2019. 215 $a1 online resource (XII, 100 p. 12 illus.) 225 1 $aSpringerBriefs in Mathematics,$x2191-8198 311 $a981-13-7074-5 330 $aThis book explains the notion of Brakke?s mean curvature flow and its existence and regularity theories without assuming familiarity with geometric measure theory. The focus of study is a time-parameterized family of k-dimensional surfaces in the n-dimensional Euclidean space (1 ? k < n). The family is the mean curvature flow if the velocity of motion of surfaces is given by the mean curvature at each point and time. It is one of the simplest and most important geometric evolution problems with a strong connection to minimal surface theory. In fact, equilibrium of mean curvature flow corresponds precisely to minimal surface. Brakke?s mean curvature flow was first introduced in 1978 as a mathematical model describing the motion of grain boundaries in an annealing pure metal. The grain boundaries move by the mean curvature flow while retaining singularities such as triple junction points. By using a notion of generalized surface called a varifold from geometric measure theory which allows the presence of singularities, Brakke successfully gave it a definition and presented its existence and regularity theories. Recently, the author provided a complete proof of Brakke?s existence and regularity theorems, which form the content of the latter half of the book. The regularity theorem is also a natural generalization of Allard?s regularity theorem, which is a fundamental regularity result for minimal surfaces and for surfaces with bounded mean curvature. By carefully presenting a minimal amount of mathematical tools, often only with intuitive explanation, this book serves as a good starting point for the study of this fascinating object as well as a comprehensive introduction to other important notions from geometric measure theory. 410 0$aSpringerBriefs in Mathematics,$x2191-8198 606 $aFunctions of real variables 606 $aDifferential equations, Partial 606 $aPotential theory (Mathematics) 606 $aGeometry, Differential 606 $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aPotential Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12163 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 615 0$aFunctions of real variables. 615 0$aDifferential equations, Partial. 615 0$aPotential theory (Mathematics) 615 0$aGeometry, Differential. 615 14$aReal Functions. 615 24$aPartial Differential Equations. 615 24$aPotential Theory. 615 24$aDifferential Geometry. 676 $a515.8 700 $aTonegawa$b Yoshihiro$4aut$4http://id.loc.gov/vocabulary/relators/aut$0781844 906 $aBOOK 912 $a9910350246903321 996 $aBrakke's Mean Curvature Flow$91733849 997 $aUNINA