论文标题
弹性流的Lojasiewicz-Simon不平等
The Lojasiewicz-Simon inequality for the elastic flow
论文作者
论文摘要
我们将平滑沉浸式封闭曲线的弹性能量定义为$ \ mathbb {r}^n $作为长度的长度和$ l^2 $ norm的弹性能量，相对于长度度量。我们证明，这种能量的$ l^2 $差流平滑地渐近地收敛到临界点。我们的目标之一是目前以相当简洁且通用的方式应用了Lojasiewicz-Simon不平等，这是证明的核心。
We define the elastic energy of smooth immersed closed curves in $\mathbb{R}^n$ as the sum of the length and the $L^2$-norm of the curvature, with respect to the length measure. We prove that the $L^2$-gradient flow of this energy smoothly converges asymptotically to a critical point. One of our aims was to the present the application of a Lojasiewicz-Simon inequality, which is at the core of the proof, in a quite concise and versatile way.
