Abstract

We reveal some new evolutionary structures of convex pentagons on a C2C^2 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 C2C^2 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.

Author information

Contact details are reproduced from the original publication and may be historical.

Anastasios N. Zachos

University of Patras, Dept. of Mathematics, 26500 Rion, Greece

azachos@gmail.com

Keywords

  • Weighted Fermat-Torricelli problem
  • Steiner minimal tree
  • convex pentagons
  • surface
  • dendrite

Mathematics Subject Classification

51E12, 52A10, 52A55, 51E10

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Suggested citation

A. N. Zachos. “An Evolutionary Structure of Convex Pentagons on a C^2 Complete Surface and a Creation Principle of some Weighted Dendrites of Order Three.” Journal of Convex Analysis 20 (2013), No. 4, 1043–1073. https://doi.org/10.68381/jca20057

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Published by Heldermann Verlag, 2013. Rights now held by Banach Press LLC.