JournalscmhVol. 95, No. 1pp. 167–182

Non-existence of geometric minimal foliations in hyperbolic three-manifolds

  • Michael Wolf

    Rice University, Houston, USA

  • Yunhui Wu

    Tsinghua University, Beijing, China
Non-existence of geometric minimal foliations in hyperbolic three-manifolds cover
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Abstract

We show that every three-dimensional hyperbolic manifold admits no locally geometric 1-parameter family of closed minimal surfaces. Here such a geometric family has normal deformations at a point that depend only the principal curvatures of that leaf at that point.

Cite this article

Michael Wolf, Yunhui Wu, Non-existence of geometric minimal foliations in hyperbolic three-manifolds. Comment. Math. Helv. 95 (2020), no. 1, pp. 167–182

DOI 10.4171/CMH/484