The vanishing exponent limit for motion by a power of mean curvature

Abstract

We discuss limit behavior of solutions to level set equation of power mean curvature flow as the exponent tends to zero, which has important applications to shape analysis in image processing. A formal limit yields a fully nonlinear singular equation that describes the motion of a surface by the sign of its mean curvature.We justify the convergence by providing a definition of viscosity solutions to the limit equation and establishing a comparison principle.