If 
has period 
,
is 
,
and
 |
(1)
|
then
 |
(2)
|
unless
 |
(3)
|
(Hardy et al. 1988).
Another inequality attributed to Wirtinger involves the Kähler form, which in 
can be written
 |
(4)
|
Given 
vectors 
in 
,
let 
denote the oriented 
-dimensional parallelepiped
and 
its 
-dimensional
volume. Then
 |
(5)
|
with equality iff the vectors span a 
-dimensional complex subspace of 
, and they are positively oriented. Here, 
is the 
th exterior power for 
, and the orientation of
a complex subspace
is determined by its complex structure.
