# Families of Minimal Surfaces in $$\mathbb {H}^2 \times \mathbb {R}$$ Foliated by Arcs and Their Jacobi Fields

@article{Ferrer2017FamiliesOM, title={Families of Minimal Surfaces in \$\$\mathbb \{H\}^2 \times \mathbb \{R\}\$\$ Foliated by Arcs and Their Jacobi Fields}, author={Leonor Ferrer and Francisco Jos'e Plaza Mart'in and Rafe Mazzeo and Magdalena Rodr'iguez}, journal={arXiv: Differential Geometry}, year={2017}, pages={67-88} }

This note provides some new perspectives and calculations regarding an interesting known family of minimal surfaces in \(\mathbb {H}^2 \times \mathbb {R}\). The surfaces in this family are the catenoids, parabolic catenoids and tall rectangles. Each is foliated by either circles, horocycles or circular arcs in horizontal copies of \(\mathbb {H}^2\). All of these surfaces are well-known, but the emphasis here is on their unifying features and the fact that they lie in a single continuous family… Expand

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