Title: Existence of closed embedded curves of constant curvature via min-max
Authors: Lorenzo Sarnataro, Douglas Stryker
Categories: math.DG math.DS
Comments: 26 pages
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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.
\\ ( https://arxiv.org/abs/2306.04840 , 29kb)