Index estimates for harmonic Gauss maps
| Autor: | de Carvalho, Alcides, Cavalcante, Marcos P., Costa-Filho, Wagner, de Oliveira, Darlan |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $\Sigma$ denote a closed surface with constant mean curvature in $\mathbb{G}^3$, a 3-dimensional Lie group equipped with a bi-invariant metric. For such surfaces, there is a harmonic Gauss map which maps values to the unit sphere within the Lie algebra of $\mathbb{G}$. We prove that the energy index of the Gauss map of $\Sigma$ is bounded below by its topological genus. We also obtain index estimates in the case of complete non compact surfaces. Comment: 11 pages |
| Databáze: | arXiv |
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