Curves in Banach spaces which allow a C^1,BV parametrization or a parametrization with finite convexity

Abstract

We give a complete characterization of those curves in a Banach space which allow an equivalent C^1,BV parametrization (i.e. a C^1 parametrization whose derivative has bounded variation) or a parametrization with bounded convexity.

Keywords

• curve in Banach spaces
• C^1,BV parametrization
• parametrization with bounded convexity