Geodesic
An Evolutionary Structure of Convex Pentagons on a C2 Complete Surface and a Creation Principle of some Weighted Dendrites of Order Three
Journal of convex analysis, Tome 20 (2013) no. 4, pp. 1043-1073.

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We reveal some new evolutionary structures of convex pentagons on a C2 surface in the three dimensional Euclidean Space which is hidden on the notion of plasticity of weighted convex pentagons and quadrilaterals. We prove a creation principle for a weighted dendrite of order 3 on a C2 surface which is derived by decreasing the degree of plasticity of weighted convex pentagons from 2 to 1. The creation principle of weighted dendrites of order 3 characterize the process of creation of various leaf tree types on surfaces.
Classification : 51E12, 52A10, 52A55, 51E10
Mots-clés : Weighted Fermat-Torricelli problem, Steiner minimal tree, convex pentagons, surface, dendrite 
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     author = {A. N. Zachos},
     title = {An {Evolutionary} {Structure} of {Convex} {Pentagons} on a {C\protect\textsuperscript{2}} {Complete} {Surface} and a {Creation} {Principle} of some {Weighted} {Dendrites} of {Order} {Three}},
     journal = {Journal of convex analysis},
     pages = {1043--1073},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2013},
     url = {http://geodesic.mathdoc.fr/item/JCA_2013_20_4_JCA_2013_20_4_a9/}
}
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A. N. Zachos. An Evolutionary Structure of Convex Pentagons on a C2 Complete Surface and a Creation Principle of some Weighted Dendrites of Order Three. Journal of convex analysis, Tome 20 (2013) no. 4, pp. 1043-1073. http://geodesic.mathdoc.fr/item/JCA_2013_20_4_JCA_2013_20_4_a9/