In this paper, we compute the Morse index for a free boundary minimal submanifold from data of two simpler problems. The first one is the corresponding problem with fixed boundary condition; and the second is associated with the Dirichlet-to-Neumann map for Jacobi fields. As an application, we show that the Morse index of a free boundary minimal annulus is equal to 4 if and only if it is the critical catenoid.

中文翻译：

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自由边界最小曲面的指数表征

在本文中，我们根据两个更简单问题的数据计算自由边界最小子流形的莫尔斯指数。第一个是固定边界条件的对应问题；第二个与 Jacobi 场的 Dirichlet-to-Neumann 映射相关联。作为一个应用，我们证明了自由边界最小环的莫尔斯指数等于 4 当且仅当它是临界悬链线。