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arXiv · 1910.07795

Equilibrium of Surfaces in a Vertical Force Field

Antonio Martínez·A. L. Martínez-Triviño
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Abstract

In this paper we study $\varphi$-minimal surfaces in $\mathbb{R}^3$ when the function $\varphi$ is invariant under a two-parametric group of translations. Particularly those which are complete graphs over domains in $\mathbb{R}^2$. We describe a full classification of complete flat embedded $\varphi$-minimal surfaces if $\varphi$ is strictly monotone and characterize rotational $\varphi$-minimal surfaces by its behavior at infinity when $\varphi$ has a quadratic growth.

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Antonio Martínez, A. L. Martínez-Triviño. 2019-10-17. Equilibrium of Surfaces in a Vertical Force Field. https://arxiv.org/abs/1910.07795

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