Isoperimetric Problem and Meta-fibonacci Sequences

2008 ◽  
pp. 22-30
Author(s):  
B. V. S. Bharadwaj ◽  
L. S. Chandran ◽  
Anita Das
Keyword(s):  
Isoperimetric Problem ◽  
Fibonacci Sequences

Polynomial values in Fibonacci sequences

2020 ◽  
Vol 13 (4) ◽  
pp. 597-605
Author(s):  
Adi Ostrov ◽  
Danny Neftin ◽  
Avi Berman ◽  
Reyad A. Elrazik
Keyword(s):  
Fibonacci Sequences

scholarly journals Pansu–Wulff shapes in ℍ1

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Julián Pozuelo ◽  
Manuel Ritoré
Keyword(s):  
Mean Curvature ◽  
Isoperimetric Problem ◽  
Variational Formula ◽  
Geodesic Curvature ◽  
Vertical Axis ◽  
Singular Part ◽  
Tangent Plane ◽  
Curvature Function ◽  
Invariant Norm ◽  
The First Variation

Abstract We consider an asymmetric left-invariant norm ∥ ⋅ ∥ K {\|\cdot\|_{K}} in the first Heisenberg group ℍ 1 {\mathbb{H}^{1}} induced by a convex body K ⊂ ℝ 2 {K\subset\mathbb{R}^{2}} containing the origin in its interior. Associated to ∥ ⋅ ∥ K {\|\cdot\|_{K}} there is a perimeter functional, that coincides with the classical sub-Riemannian perimeter in case K is the closed unit disk centered at the origin of ℝ 2 {{\mathbb{R}}^{2}} . Under the assumption that K has C 2 {C^{2}} boundary with strictly positive geodesic curvature we compute the first variation formula of perimeter for sets with C 2 {C^{2}} boundary. The localization of the variational formula in the non-singular part of the boundary, composed of the points where the tangent plane is not horizontal, allows us to define a mean curvature function H K {H_{K}} out of the singular set. In the case of non-vanishing mean curvature, the condition that H K {H_{K}} be constant implies that the non-singular portion of the boundary is foliated by horizontal liftings of translations of ∂ ⁡ K {\partial K} dilated by a factor of 1 H K {\frac{1}{H_{K}}} . Based on this we can define a sphere 𝕊 K {\mathbb{S}_{K}} with constant mean curvature 1 by considering the union of all horizontal liftings of ∂ ⁡ K {\partial K} starting from ( 0 , 0 , 0 ) {(0,0,0)} until they meet again in a point of the vertical axis. We give some geometric properties of this sphere and, moreover, we prove that, up to non-homogeneous dilations and left-translations, they are the only solutions of the sub-Finsler isoperimetric problem in a restricted class of sets.

AN ISOPERIMETRIC RESULT FOR THE GAUSSIAN MEASURE AND UNCONDITIONAL SETS

2001 ◽  
Vol 33 (4) ◽  
pp. 408-416 ◽  
Author(s):  
F. BARTHE
Keyword(s):  
Gaussian Measure ◽  
Isoperimetric Problem ◽  
Boundary Measure

The paper studies an isoperimetric problem for the Gaussian measure and coordinatewise symmetric sets. The notion of boundary measure corresponding to the uniform enlargement is considered, and it is proved that symmetric strips or their complements have minimal boundary measure.

Nature-Inspired Quasicrystal SRG Using Fibonacci Sequences in Photo-Reconfiguration on Azo Polymer Films

2018 ◽  
Vol 26 (11) ◽  
pp. 1042-1047 ◽  
Author(s):  
Kang-Han Kim ◽  
Kuk Young Cho ◽  
Yong-Cheol Jeong
Keyword(s):  
Polymer Films ◽  
Azo Polymer ◽  
Fibonacci Sequences

The isoperimetric problem

Resonance ◽  
1997 ◽  
Vol 2 (9) ◽  
pp. 65-68 ◽  
Author(s):  
Alladi Sitaram
Keyword(s):  
Isoperimetric Problem
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