A self-shrinker for mean curvature flow is a submanifold whose mean curvature vector satisfies
 |
where 
is the normal projection of the position vector. It generates the solution 
for 
. With the trace normalization of mean
curvature, a round 
-hypersphere of radius 
centered at the origin is a self-shrinker.
In 
, the round sphere
of radius 2 and the right
circular cylinder of radius 
are examples.
