Rectifiability Property for Plane Paths and Descent Curves

Nico Lombardi, Marco Longinetti (), Paolo Manselli and Adriana Venturi
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Nico Lombardi: Vienna University of Technology
Marco Longinetti: Università di Firenze
Paolo Manselli: Università di Firenze
Adriana Venturi: Università di Firenze

Journal of Optimization Theory and Applications, 2020, vol. 187, issue 1, No 14, 294-302

Abstract: Abstract A family of plane, oriented and continuous paths depending on a fixed real positive number is considered. For any point on the path, the previous points lie out of any disk with same radius, having interior normal in a suitable tangent cone to the path. These paths are locally descent curves of a nested family sets of same positive reach. Avoiding any smoothness requirements, we get angle estimate and not intersection property. Afterwards, we are able to estimate the length and detour of this curve.

Keywords: Steepest descent curves; Sets with positive reach; Length of curves; Detour; Primary: 28A75; 52A30; Secondary: 34A26; 34A60 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01739-1

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