论文标题
$ \ infty $ - 弹性问题在Riemannian歧管上
The $\infty$-elastica problem on a Riemannian manifold
论文作者
论文摘要
我们考虑以下问题：在所有具有固定长度以及固定端点和切线的曲线中，在任何给定的完整的Riemannian歧管$（m，g）$中，在端点上，将曲率的$ l^\ infty $规范最小化。我们表明，该问题的解决方案以及更广泛的曲线必须满足二阶ode系统。从该系统中，我们获得了一些有关曲线行为的几何信息。
We consider the following problem: on any given complete Riemannian manifold $(M,g)$, among all curves which have fixed length as well as fixed end-points and tangents at the end-points, minimise the $L^\infty$ norm of the curvature. We show that the solutions of this problem, as well as a wider class of curves, must satisfy a second order ODE system. From this system we obtain some geometric information about the behaviour of the curves.
