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
