Existence of curves with constant geodesic curvature in a Riemannian 2-sphere

Da Rong Cheng; Xin Zhou

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arXiv · 2106.12374

Existence of curves with constant geodesic curvature in a Riemannian 2-sphere

Da Rong Cheng·Xin Zhou

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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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Da Rong Cheng, Xin Zhou. 2021-06-23. Existence of curves with constant geodesic curvature in a Riemannian 2-sphere. https://arxiv.org/abs/2106.12374

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