This book is intended to be a self-contained introduction to
analytic foundations of a level set method for various surface
evolution equations including curvature ?ow equations. These
equations are important in various ?elds including material
sciences, image processing and di?erential geometry. The goal of
this book is to introduce a generalized notion of solutions
allowing singularities and solve the initial-value problem
globally-in-time in a generalized sense. Various equivalent
de?nitions of solutions are studied. Several new results on
equivalence are also presented.
Wepresentherearathercompleteintroductiontothetheoryofviscosityso-
tionswhichis a keytoolforthe levelsetmethod. Alsoa
self-containedexplanation
isgivenforgeneralsurfaceevolutionequationsofthe
secondorder.Althoughmost ofthe resultsin this book aremoreor
lessknown,they arescatteredinseveralr- erences, sometimes without
proof. This book presents these results in a synthetic way with
full proofs. However, the references are not exhaustive at all. The
book is suitable for applied researchers who would like to know the
detail of the theory as well as its ?avour.No familiarity with
di?erential geometry and the theory of viscosity solutions is
required. The prerequisites are calculus, linear algebra and some
familiarity with semicontinuous functions. This book is also
suitable for upper level under graduate students who are interested
in the ?eld.
General
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