论文标题
Banach梯度流量为各种结的家族
Banach gradient flows for various families of knot energies
论文作者
论文摘要
我们长期存在BANACH梯度流，用于广义的积分Menger曲率和切线点，并为O'Hara的自我抑制潜力$ e^{α，p} $。为此，我们在稍小的空间中采用了最大斜率的曲线理论，将与这些功能相关的相应能量空间紧凑，并添加涉及对数菌株的术语，该术语控制流动（打结）循环的参数。作为先决条件，我们还证明了O'Hara的打结能量$ e^{α，p} $是不断差异的。
We establish long-time existence of Banach gradient flows for generalised integral Menger curvatures and tangent-point energies, and for O'Hara's self-repulsive potentials $E^{α,p}$. In order to do so, we employ the theory of curves of maximal slope in slightly smaller spaces compactly embedding into the respective energy spaces associated to these functionals, and add a term involving the logarithmic strain, which controls the parametrisations of the flowing (knotted) loops. As a prerequisite, we prove in addition that O'Hara's knot energies $E^{α,p}$ are continuously differentiable.
