Abstract
In this paper, we study the geometry of surfaces with the generalised simple lift property. This work generalises previous results by Bernstein and Tinaglia (J Differ Geom 102(1):1–23, 2016) and it is motivated by the fact that leaves of a minimal lamination obtained as a limit of a sequence of property embedded minimal disks satisfy the generalised simple lift property.
Highlights
Geometriae Dedicata (2020) 204:285–298 is an orientable three-manifold satisfying certain geometric conditions
One key condition is that cannot contain closed minimal surfaces. We generalise this result by taking an arbitrary orientable three-manifold and introducing the concept of the generalised simple lift property, which extends the simple lift property in [1]
We prove that leaves of a minimal lamination obtained as a limit of a sequence of properly embedded minimal disks satisfy the generalised simple lift property and we are able to restrict the topology of an arbitrary surface ⊂ with the generalised simple lift property
Summary
Throughout the paper, we will assume to be an open subset of an orientable threedimensional Riemannian manifold (M, g). If NU ( ) is regular, the map : NU ( ) → , given by the nearest point projection, is smooth and for any (q, v) ∈ T NU ( ), there is a natural splitting v = v⊥ + vT , where v⊥ is orthogonal to vT , and vT is perpendicular to the fibres of. We say that such v is δ-parallel to if. This definition extends to piece-wise C1 curves in an obvious manner
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
