Repulsive knot energies and pseudodifferential calculus for O’Hara’s knot energy family E(α), α ∈ [2, 3)
Repulsive knot energies and pseudodifferential calculus for O’Hara’s knot energy family E(α), α ∈ [2, 3)
复制标题
奥哈拉结能量族的排斥结能量和伪微分计算 E(α), α ∈ [2, 3)
DOI：
10.1002/mana.201000090
复制
发表时间：
2012
影响因子：
1
通讯作者：
P. Reiter
中科院分区：
文献类型：
--
作者：
P. Reiter
We develop a precise analysis of J. O’Hara’s knot functionals E(α), α ∈ [2, 3), that serve as self‐repulsive potentials on (knotted) closed curves. First we derive continuity of E(α) on injective and regular H2 curves and then we establish Fréchet differentiability of E(α) and state several first variation formulae. Motivated by ideas of Z.‐X. He in his work on the specific functional E(2), the so‐called Möbius Energy, we prove C∞‐smoothness of critical points of the appropriately rescaled functionals \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\tilde{E}^{(\alpha )}= {\rm length}^{\alpha -2}E^{(\alpha )}$\end{document} by means of fractional Sobolev spaces on a periodic interval and bilinear Fourier multipliers.
We develop a precise analysis of J. O’Hara’s knot functionals E(α), α ∈ [2, 3), that serve as self‐repulsive potentials on (knotted) closed curves. First we derive continuity of E(α) on injective and regular H2 curves and then we establish Fréchet differentiability of E(α) and state several first variation formulae. Motivated by ideas of Z.‐X. He in his work on the specific functional E(2), the so‐called Möbius Energy, we prove C∞‐smoothness of critical points of the appropriately rescaled functionals \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\tilde{E}^{(\alpha )}= {\rm length}^{\alpha -2}E^{(\alpha )}$\end{document} by means of fractional Sobolev spaces on a periodic interval and bilinear Fourier multipliers.