Change of the Willmore energy under infinitesimal bending of membranes

We discuss infinitesimal bending of curves and knots in R 3 . A brief overview of the results on the infinitesimal bending of curves is outlined. Change of the Willmore energy, as well as of the Möbius energy under infinitesimal bending of knots is considered. Our visualization tool devoted to visual representation of infinitesimal bending of knots is presented.Mathematics Subject Classification 2000: 53A04, 53C45, 57M25, 57M27, 78A25

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“…Curvature-based energies play a main role in the description of both physical and non-physical systems (see [3,7,10,25,26]).…”

Section: Knot Willmore Energy Change Under Infinitesimal Bendingmentioning

confidence: 99%

Infinitesimal bending of knots and energy change

Kauffman

Velimirović

Najdanović

et al. 2019

J. Knot Theory Ramifications

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“…In [9], the change of the Willmore energy of a curve under infinitesimal bending of the first order is analyzed. Many papers are dedicated to the Willmore energy of deformed surfaces (see [6,15,16]). Some other quantities are also interesting for studying at various deformations.…”

Section: Miskolc University Pressmentioning

confidence: 99%

On the Willmore energy of curves under second order infinitesimal bending

Najdanović¹,

Velimirović²

2017

MMN

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“…Infinitesimal bending of surfaces and manifolds was widely studied in [8], [11], [12], [19], [20]. Infinitesimal bending of curves at E 3 was studied at [8], [20], [21] and [22].…”

Section: Preliminariesmentioning

confidence: 99%