An Evolutionary Structure of Convex Pentagons on a C-2 Complete Surface and a Creation Principle of some Weighted Dendrites of Order Three

作者：Zachos Anastasios N^*

来源：Journal of Convex Analysis, 2013, 20(4): 1043-1073.

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

We reveal some new evolutionary structures of convex pentagons on a C-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 C-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.

• 出版日期2013