We provide sufficient conditions for a variational inequality involving the complex Monge-Amp`ere determinant and give applications to proper holomorphic mappings. We also clarify the proof of a sharp inequality about volumes of holomorphic images by placing it in this more general context.
- Complex Monge-Ampère determinant
- Plurisubharmonic functions
- Proper holomorphic mappings
- Volumes of holomorphic images
ASJC Scopus subject areas
- Applied Mathematics