2021
DOI: 10.48550/arxiv.2106.11626
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Morse-Smale complexes on convex polyhedra

Abstract: Motivated by applications in geomorphology, the aim of this paper is to extend Morse-Smale theory from smooth functions to the radial distance function (measured from an internal point), defining a convex polyhedron in 3dimensional Euclidean space. The resulting polyhedral Morse-Smale complex may be regarded, on one hand, as a generalization of the Morse-Smale complex of the smooth radial distance function defining a smooth, convex body, on the other hand, it could be also regarded as a generalization of the M… Show more

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Cited by 1 publication
(6 citation statements)
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“…In [22] we named these vectors candidate gradients at p if they are tangential to the polyhedron P . Candidate gradients were defined the same way at vertices too.…”
Section: Classification Of Convex Polyhedramentioning
confidence: 99%
See 4 more Smart Citations
“…In [22] we named these vectors candidate gradients at p if they are tangential to the polyhedron P . Candidate gradients were defined the same way at vertices too.…”
Section: Classification Of Convex Polyhedramentioning
confidence: 99%
“…In this case x is non-degenerate if H ∩ P is the (unique) face, edge or vertex of P that contains x in its relative interior. We have shown in [22] that a point x ∈ P is an equilibrium point if and only if there is no candidate gradient at x. The function r P is polyhedral Morse if all its equilibrium points are non-degenerate.…”
Section: Classification Of Convex Polyhedramentioning
confidence: 99%
See 3 more Smart Citations