Discrete thickness

• Autorzy: Sebastian Scholtes
• Języki publikacji: EN

Abstrakty

EN

We investigate the relationship between a discrete version of thickness and its smooth counterpart. These discrete energies are deffned on equilateral polygons with n vertices. It will turn out that the smooth ropelength, which is the scale invariant quotient of length divided by thickness, is the Γ-limit of the discrete ropelength for n → ∞, regarding the topology induced by the Sobolev norm ‖ · ‖ W1,∞(S1,ℝd). This result directly implies the convergence of almost minimizers of the discrete energies in a fixed knot class to minimizers of the smooth energy.Moreover,we show that the unique absolute minimizer of inverse discrete thickness is the regular n-gon.

Słowa kluczowe

EN

discrete energy; thickness; ropelength; Γ-convergence; geometric knot theory; ideal knot; Schur’s Theorem

Kategorie tematyczne

• 49J45: Methods involving semicontinuity and convergence; relaxation
• 53A04: Curves in Euclidean space
• 57M25: Knots and links in S 3
• 49Q10: Optimization of shapes other than minimal surfaces

• Wydawca: De Gruyter Open
• Czasopismo: Molecular Based Mathematical Biology
• Rocznik: 2014
• Tom: 2
• Numer: 1

Daty

otrzymano

2014-01-22

zaakceptowano

2014-07-14

online

2014-08-26

Twórcy

autor

Sebastian Scholtes

• Institut für Mathematik, RWTH Aachen University, Templergraben 55, D-52062, Aachen, Germany

Bibliografia

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Identyfikatory

DOI

10.2478/mlbmb-2014-0005