论文标题
曲率保存在空间曲线上流动的固定溶液
Stationary Solutions of the Curvature Preserving Flow on Space Curves
论文作者
论文摘要
我们研究曲线上的几何流，沉浸在$ \ mathbb {r}^3 $中，具有严格的阳性扭转。 Evolution方程由$$ x_ {t} = \ frac {1} {\sqrtτ} \ textbf {b} $$，其中$τ$是扭力，$ \ textbf {b} $是单位binormal binormal vector。在恒定曲率的情况下，我们找到所有固定溶液，并将PDE线性化，以围绕固定溶液的扭转，以承认明确的公式。之后，我们证明了$ l^2（\ mathbb {r}）$的固定解决方案的线性稳定性，与螺旋相对应持续曲率和恒定扭转的螺旋。
We study a geometric flow on curves, immersed in $\mathbb{R}^3$, that have strictly positive torsion. The evolution equation is given by $$X_{t}=\frac{1}{\sqrtτ} \textbf{B}$$ where $τ$ is the torsion and $\textbf{B}$ is the unit binormal vector. In the case of constant curvature, we find all of the stationary solutions and linearize the PDE for torsion around stationary solutions admitting an explicit formula. Afterwards, we prove the $L^2(\mathbb{R})$ linear stability of the stationary solutions corresponding to helices with constant curvature and constant torsion.
