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2016 Bounding Regions to Plane Steepest Descent Curves of Quasiconvex Families
Marco Longinetti, Paolo Manselli, Adriana Venturi
J. Appl. Math. 2016: 1-17 (2016). DOI: 10.1155/2016/4873276


Two-dimensional steepest descent curves (SDC) for a quasiconvex family are considered; the problem of their extensions (with constraints) outside of a convex body K is studied. It is shown that possible extensions are constrained to lie inside of suitable bounding regions depending on K. These regions are bounded by arcs of involutes of K and satisfy many inclusions properties. The involutes of the boundary of an arbitrary plane convex body are defined and written by their support function. Extensions SDC of minimal length are constructed. Self-contracting sets (with opposite orientation) are considered: necessary and/or sufficient conditions for them to be subsets of SDC are proved.


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Marco Longinetti. Paolo Manselli. Adriana Venturi. "Bounding Regions to Plane Steepest Descent Curves of Quasiconvex Families." J. Appl. Math. 2016 1 - 17, 2016.


Received: 26 February 2016; Accepted: 17 April 2016; Published: 2016
First available in Project Euclid: 13 August 2016

zbMATH: 07037278
MathSciNet: MR3534138
Digital Object Identifier: 10.1155/2016/4873276

Rights: Copyright © 2016 Hindawi


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