cam a22 5 4500 569341876 CHVBK 20200527061627.0 m d cr |n |||||||| 190409s2019 si |||| s 0 0|eng d 978-981-13-7075-5 978-981-13-7074-8 (print) 978-981-13-7076-2 (print) 10.1007/978-981-13-7075-5 doi (SERSOL)ssj0002135851 (WaSeSS)ssj0002135851 WaSeSS QA331.5 PBKB bicssc MAT034000 bisacsh 515.8 23 Tonegawa Yoshihiro author aut http://id Brakke's Mean Curvature Flow [Elektronische Daten] An Introduction by Yoshihiro Tonegawa 1st ed. 2019. Singapore Springer Singapore Imprint: Springer 2019 1 online resource (XII, 100 p. 12 illus.) online resource text txt rdacontent/ger computer c rdamedia/ger online resource cr rdacarrier/ger text file PDF rda SpringerBriefs in Mathematics 2191-8198 SpringerBriefs in Mathematics 2191-8198 Lizenzbedingungen können den Zugang einschränken. License restrictions may limit access. This 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. Functions of real variables Partial differential equations Potential theory (Mathematics) Differential geometry SpringerLink (Online service) Printed edition 9789811370748 Printed edition 9789811370762 https://link.springer.com/10.1007/978-981-13-7075-5 Uni Basel: Volltext Springer Mathematics and Statistics eBooks 2019 English/International E-Books von 360MarcUpdates PBKB thema IDSBB 100 1- Tonegawa Yoshihiro author aut http://id IDSBB 490 1- SpringerBriefs in Mathematics 2191-8198 IDSBB 710 2- SpringerLink (Online service) IDSBB 776 08 Printed edition 9789811370748 IDSBB 776 08 Printed edition 9789811370762 IDSBB 856 40 https://link.springer.com/10.1007/978-981-13-7075-5 Uni Basel: Volltext SWISSBIB 569184886 BK020053 XK020053 XK020000 IDSBB A145 A145 145VT NELA1451907