Limit behaviour of constant distance boundaries of Jordan curves

Abstract

For a Jordan curve Γ in the complex plane, its constant distance boundary Γλ is an inflated version of Γ. A flatness condition, (1/2,r0)-chordal property, guarantees that Γλ is a Jordan curve when λ is not too large. We prove that Γλ converges to Γ, as λ approaching to 0, in the sense of Hausdorff distance if Γ has the (1/2,r0)-chordal property.

Keywords

• constant distance boundary
• hausdorff distance
• jordan curve