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Showing 1 to 2 of 2 for “"Knot Energies"”.
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Repulsive knot energies and pseudodifferential calculus : rigorous analysis and regularity theory for O'Hara's knot energy family E (alpha), alpha in [2,3)
In this thesis, we consider J. O'Hara's knot functionals E^(alpha), $alphain[2,3)$, proving Fréchet differentiability and $C^infty$ regularity of critical points. Using some ideas of Z.-X. He and filling major gaps in his investigation of the Möbius Energy E^(2), we furnish a rigorous proof of an …
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Error Bounds Between the Minimum Distance Energy of an Equilateral Knot and the Mobius Energy of an Inscribed Smooth Knot
This thesis explores mathematical knots and energy functions defined for them. Specifically, we explore the question of whether or not the Minimum Distance Energy of an equilateral knot is close to the Mobius Energy of a smooth knot where the smooth knot is inscribed in the equilateral knot in a …