Monographs in Mathematics: A Level Set Approach

Giga, Yoshikazu; Liu, Qing

This monograph presents a self-contained introduction to the analytic foundation of a level set approach for various surface evolution equations, including curvature flow equations. These equations are important in many applications, such as material sciences, image processing, and differential geometry. The goal is to introduce a generalized notion of solutions allowing singularities and to solve the initial-value problem globally-in-time in a generalized sense. 

For the Second Edition, new chapters have been added that describe a recent approach to surface evolution equations based on deterministic discrete two-person games. This game-theoretic interpretation is used to discuss the fattening phenomenon for the curvature flow equation and to provide an alternative proof for convexity preserving properties.

This text is suitable for applied researchers who would like to know the detail of the theory, as well as its flavor; it is also suitable for graduate students interested in the field. Prerequisites include calculus, linear algebra, and some familiarity with semicontinuous functions. Familiarity with differential geometry and the theory of viscosity solutions is not required.  

Details

Published by: Birkhäuser

Publication Date: 2026-09-16

Format: Hardcover

ISBN-13: 9783032203021

DOI:

Dimensions: 235cm x155cm

Pages: 362