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Uniqueness of H-surfaces in {mathbb{H}}^2 times mathbb{R},{{vert Hvert leq 1/2}} , with boundary one or two parallel horizontal circles |
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| Authors: | Barbara Nelli Ricardo Sa Earp Walcy Santos Eric Toubiana |
| Affiliation: | 1. Dipartimento di Matematica, Universitá di L’Aquila, via Vetoio - Loc. Coppito, L’Aquila, 67010, Italy 2. Departamento de Matemática, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, RJ, 22453-900, Brazil 3. Instituto de Matemtica, Universidade Federal do Rio de Janeiro, Av. Brigadeiro Trompowsky, s/n Cidade Universitria, Ilha do Fund?o, Caixa Postal 68530, Rio de Janeiro, RJ, 21945-970, Brazil 4. Institut de Mathématiques de Jussieu, Université Paris VII, Denis Diderot, Case 7012, 2 Place Jussieu, 75251, Paris Cedex 05, France |
| Abstract: | We prove that a H-surface M in ${mathbb{H}}^2 times {mathbb{R}} ,vert Hvert leq 1/2$ , inherits the symmetries of its boundary $partial M,$ when $partial M$ is either a horizontal curve with curvature greater than one or two parallel horizontal curves with curvature greater than one, whose distance is greater or equal to π. Furthermore we prove that the asymptotic boundary of a surface with mean curvature bounded away from zero consists of parts of straight lines, provided it is sufficiently regular. |
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