The complex analogue of Diecke's Theorem and Brickell's Theorem in
real Finsler geometry. Complex Finsler structures naturally satisfy the complex
homogeneous Monge-Ampere equation and the analogue of Diecke's Theorem and
Brickell's Theorem can be put in the frame work of the classification of
complex manifolds admitting an exhaustion function satisfying the complex
homogeneous Monge-Ampere equation.