Minimal Surfaces in a cylindrical region of R3 with a Randers metric

• Autores: Rosangela María da Silva, Keti Tenenblat
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 37, Nº 3, 2011, págs. 745-771
• Idioma: inglés
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• Resumen

  • We consider the Euclidean metric of R3 perturbed by a rotation. This Finsler space, M3, is the open region of R3 bounded by a cylinder with a Randers metric. Using the Busemann-Hausdorff volume form, we prove that the only minimal surfaces of rotation in this space are the catenoids contained in M3, generated by the rotation of a catenary around the axis of the cylinder. There are no minimal surfaces of rotation whose rotational axis is different from the axis of the cylinder. Moreover, we obtain the partial differential equations that characterize the minimal surfaces in M3 that are the graph of a function. We prove that the only planar regions which are minimal M3 are the open disks bounded by the parallels of the cylinder and the strips of planes generated by the intersection of M3 with the planes of R3 that contain the cylinder axis.