Complete minimal submanifolds with nullity in Euclidean space

作者：Dajczer Marcos; Kasioumis Theodoros; Savas Halilaj Andreas^*; Vlachos Theodoros

来源：Mathematische Zeitschrift, 2017, 287(1-2): 481-491.

DOI：10.1007/s00209-016-1833-4

• Minimal submanifold
• Relative nullity foliation
• Maximum principle

In this paper, we investigate minimal submanifolds in Euclidean space with positive index of relative nullity. Let be a complete Riemannian manifold and let be a minimal isometric immersion with index of relative nullity at least at any point. We show that if the Omori-Yau maximum principle for the Laplacian holds on , for instance, if the scalar curvature of does not decrease to too fast or if the immersion f is proper, then the submanifold must be a cylinder over a minimal surface.

• 出版日期2017-10