# On the topology of surfaces with the generalised simple lift property

@article{Tripaldi2020OnTT, title={On the topology of surfaces with the generalised simple lift property}, author={Francesca Tripaldi}, journal={Geometriae Dedicata}, year={2020}, volume={204}, pages={285 - 298} }

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.

## References

SHOWING 1-10 OF 20 REFERENCES

### The space of embedded minimal surfaces of fixed genus in a 3-manifold III; Planar domains

- Mathematics
- 2002

This paper is the third in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed 3-manifold. In [CM3]–[CM5] we describe the case where…

### Limiting behavior of sequences of properly embedded minimal disks

- Mathematics
- 2017

We develop a theory of "minimal $\theta$-graphs" and characterize the behavior of limit laminations of such surfaces, including an understanding of their limit leaves and their curvature blow-up…

### Embedded minimal disks with prescribed curvature blowup

- Mathematics
- 2004

We construct a sequence of compact embedded minimal disks in a ball in R 3 , whose boundaries lie in the boundary of the ball, such that the curvature blows up only at a prescribed discrete (and…

### Genus-one helicoids from a variational point of view

- Mathematics
- 2006

In this paper, we use variational methods to prove existence of a complete, properly embedded, genus-one minimal surface that is asymptotic to a helicoid at infinity. We also prove some new…

### Topological Type of Limit Laminations of Embedded Minimal Disks

- Mathematics
- 2013

We consider two natural classes of minimal laminations in three-manifolds. Both classes may be thought of as limits - in different senses - of embedded minimal disks. In both cases, we prove that,…

### The space of embedded minimal surfaces of fixed genus in a 3-manifold V; Fixed genus

- Mathematics
- 2005

This paper is the fifth and final in a series on embedded minimal surfaces. Following our earlier papers on disks, we prove here two main structure theorems for \itnonsimply connected embedded…

### A Minimal Lamination with Cantor Set-Like Singularities

- Mathematics
- 2009

Given a compact closed subset $M$ of a line segment in $\mathbb{R}^3$, we construct a sequence of minimal surfaces $\Sigma_k$ embedded in a neighborhood $C$ of the line segment that converge smoothly…

### Embedded minimal disks: Proper versus nonproper—global versus local

- Mathematics
- 2002

We construct a sequence of (compact) embedded minimal disks in a ball in R 3 with boundaries in the boundary of the ball and where the curvatures blow up only at the center. The sequence converges to…

### The uniqueness of the helicoid

- Mathematics
- 2005

In this paper we will discuss the geometry of finite topology properly embedded minimal surfaces M in R3. M of finite topology means M is homeomorphic to a compact surface M̂ (of genus k and empty…

### A Minimal Lamination of the Unit Ball with Singularities along a Line Segment

- Mathematics
- 2009

We construct a sequence of compact embedded minimal disks in the unit ball in Euclidean 3-space whose boundaries are in the boundary of the ball and where the curvatures blow up at every point of a…