## Abstract

In this paper, we prove several results on the geometry of surfaces immersed in with small or bounded norm of . For instance, we prove that if the norm of and the norm of , , are sufficiently small, then such a surface is graphical away from its boundary. We also prove that given an embedded disk with bounded norm of , not necessarily small, then such a disk is graphical away from its boundary, provided that the norm of is sufficiently small, . These results are related to previous work of Schoen-Simon (Surfaces with quasiconformal Gauss map. Princeton University Press, Princeton, vol 103, pp 127-146, 1983) and Colding-Minicozzi (Ann Math 160:69-92, 2004).

Original language | English |
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Pages (from-to) | 159-186 |

Number of pages | 28 |

Journal | ANNALS OF GLOBAL ANALYSIS AND GEOMETRY |

Volume | 46 |

Issue number | 2 |

DOIs | |

Publication status | Published - Aug 2014 |

## Keywords

- CURVATURE
- SPACE