The Reflection Principle for One-dimensional Quasiminimizers

Abstract: In this paper the reflection-extension of one-dimensional quasiminimizers is studied.A brief introduction to quasiminimizers, focused on the one-dimensional ones, is given.The main result of the study concerns the size of the quasiminimizing constant of theextended function relative to the unextended one. Previous work by O. Martio gives anupper bound for this relation. This bound is lowered, and the new bound is proven to besharp.Sharp quasiminimizer constants are calculated for a few simple functions and theirreflection-extensions.