Abstract:We prove the existence of immersed closed curves of constant geodesic curvature in an arbitrary Riemannian 2-sphere for almost every prescribed curvature. To achieve this, we develop a min-max scheme for a weighted length functional.

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中文翻译：

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黎曼 2 球体中具有恒定测地曲率的曲线的存在性

摘要：我们证明了在任意黎曼 2 球体中，对于几乎所有规定的曲率，都存在恒定测地曲率的浸没闭合曲线。为了实现这一点，我们为加权长度泛函开发了一个最小-最大方案。

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