%0 Journal Article %T Calabi-Yau Problem for Legendrian curves in C^3 and applications %A Francisco Martin %A Masaaki Umehara %A Kotaro Yamada %J Mathematics %D 2011 %I arXiv %X We construct a complete, bounded Legendrian immersion in C^3. As direct applications of it, we show the first examples of a weakly complete bounded flat front in hyperbolic 3-space, a weakly complete bounded flat front in de Sitter 3-space, and a weakly complete bounded improper affine front in R^3. %U http://arxiv.org/abs/1107.0106v2