Guardat en:
| Autor principal: | |
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| Format: | Preprint |
| Publicat: |
2020
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| Matèries: | |
| Accés en línia: | https://arxiv.org/abs/2004.05532 |
| Etiquetes: |
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Taula de continguts:
- We revisit the classical problem due to Weyl, as well as its generalisations, concerning the isometric immersions of $\mathbb{S}^2$ into simply-connected $3$-dimensional Riemannian manifolds with non-negative Gauss curvature. A sufficient condition is exhibited for the existence of global $C^{1,1}$-isometric immersions. Our developments are based on the framework à la Labourie (Immersions isométriques elliptiques et courbes pseudo-holomorphes, J. Diff. Geom. 30 (1989), 395--424) of studying isometric immersions using $J$-holomorphic curves. We obtain along the way a generalisation of a classical theorem due to Heinz and Pogorelov.