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arXiv · 2202.00942

Length-minimizing level curves via calibrations

Kwok-Kun Kwong·Hojoo Lee
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Abstract

We present an elementary criterion to show the length-minimizing property of geodesics for a large class of conformal metrics. In particular, we prove the length-minimizing property of level curves of harmonic functions and the length-minimizing property of a family of the conic sections with the eccentricity $\varepsilon$ in the upper half plane endowed with the conformal metric $ \left( {\varepsilon}^{2} + \frac{1}{\;{y^2} \;} \right) \left(dx^{2} + dy^{2} \right)$.

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Kwok-Kun Kwong, Hojoo Lee. 2022-02-02. Length-minimizing level curves via calibrations. https://arxiv.org/abs/2202.00942

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