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arXiv · 2306.04840

Existence of closed embedded curves of constant curvature via min-max

Lorenzo Sarnataro·Douglas Stryker
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Abstract

We find conditions under which Almgren-Pitts min-max for the prescribed geodesic curvature functional in a closed oriented Riemannian surface produces a closed embedded curve of constant curvature. In particular, we find a closed embedded curve of any prescribed constant curvature in any metric on $S^2$ with $1/8$-pinched Gaussian curvature.

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Lorenzo Sarnataro, Douglas Stryker. 2023-06-08. Existence of closed embedded curves of constant curvature via min-max. https://arxiv.org/abs/2306.04840

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