Bounding Regions to Plane Steepest Descent Curves of Quasiconvex Families
Keyword(s):
Two-dimensional steepest descent curves (SDC) for a quasiconvex family are considered; the problem of their extensions (with constraints) outside of a convex bodyKis studied. It is shown that possible extensions are constrained to lie inside of suitable bounding regions depending onK. These regions are bounded by arcs of involutes of∂Kand 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.
1951 ◽
Vol 47
(1)
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pp. 245-247
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Keyword(s):
2005 ◽
Vol 42
(3)
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pp. 253-264
Keyword(s):
1969 ◽
Vol 76
(1)
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pp. 54-55
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2012 ◽
Vol 54
(2)
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pp. 643-649