A bent helicoid is a minimal surface that winds around a curved axis, resembling a helicoid bent along that axis (Meeks and Weber 2007). Such surfaces can be constructed from a real analytic curve and a rapidly rotating normal vector using the Björling curve construction.
For the unit circle, take
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
is a positive integer and 
is the prescribed normal
vector. The resulting complete immersed
minimal annuli have total
curvature 
. For large 
, compact annular neighborhoods of the core circle
are embedded, although the complete surfaces
have self-intersections (Meeks and Weber 2007).
