Estimates for the Constant Mean Curvature Dirichlet Problem on Catenoids
| Autor: | Kleene, Stephen J. |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this article, we solve the constant mean curvature dirichlet problem on catenoidal necks with small scale in $\mb{R}^3$. The solutions are found in exponentially weighted H\"older spaces with non-integer weight and are a-priori bounded by a uniform constant times $r^{1 + \gamma}$, where $r$ denotes the distance to the axis of the neck and where $\gamma$ belongs to the interval $(0, 1)$. By comparing the solutions with their limits on the disk, we improve the estimate to $\gamma =1$. As a corollary, we prove differentiability of solutions in $\tau$ down to $\tau = 0$. The surfaces we construct have applications to gluing constructions. Comment: 30 pages, no figures |
| Databáze: | arXiv |
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