Content deleted Content added
→Examples: ddbar lemma |
|||
Line 35:
'''Relation to Kähler manifold:''' On n-dimensional complex Euclidean space <math>\mathbb{C}^n</math> , <math>f(z) = |z|^2</math> is plurisubharmonic. In fact, <math>\sqrt{-1}\partial\overline{\partial}f</math> is equal to the standard [[Kähler form]] on <math>\mathbb{C}^n</math> up to constant multiples. More generally, if <math>g</math> satisfies
::<math>\sqrt{-1}\partial\overline{\partial}g=\omega</math>
for some Kähler form <math>\omega</math>, then <math>g</math> is plurisubharmonic, which is called Kähler potential. These can be readily generated by applying the [[ddbar lemma]] to Kähler forms on a Kähler manifold.
'''Relation to Dirac Delta:''' On 1-dimensional complex Euclidean space <math>\mathbb{C}^1</math> , <math>u(z) = \log(z)</math> is plurisubharmonic. If <math>f</math> is a C<sup>∞</sup>-class function with [[compact support]], then [[Cauchy integral formula]] says
| |||