ABSTRACT
Let be the class of plane, oriented, rectifiable curves
, such that for almost every
, the part of
preceding x is outside of the open circle of radius R, centered in
, where
is the unit tangent vector at x. Geometrical properties of the curves
are proved; it is shown also that the length of a regular curve
is bounded by a constant depending upon R and the diameter of
only. The curves
turn out to be steepest descent curves for real-valued functions with sublevel sets of reach greater than R.
AMS SUBJECT CLASSIFICATIONS:
Notes
No potential conflict of interest was reported by the authors.