Bubbles with constant mean curvature, and almost constant mean curvature, in the hyperbolic space
| Autor: | Cora, G., Musina, R. |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | Given a constant $k>1$, let $Z$ be the family of round spheres of radius $\textrm{artanh}(k^{-1})$ in the hyperbolic space $\mathbb{H}^3$, so that any sphere in $Z$ has mean curvature $k$. We prove a crucial nondegeneracy result involving the manifold $Z$. As an application, we provide sufficient conditions on a prescribed function $\phi$ on $\mathbb{H}^3$, which ensure the existence of a ${\cal C}^1$-curve, parametrized by $\varepsilon\approx 0$, of embedded spheres in $\mathbb{H}^3$ having mean curvature $k +\varepsilon\phi$ at each point. Comment: 31 pages |
| Databáze: | arXiv |
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