Complex geodesics and complex Monge-Ampere equations with boundary singularity

We will talk about the existence and uniqueness of complex geodesics with prescribed boundary value and direction in strongly linearly convex domains with $C^3$-boundary, and the associated boundary spherical representation of such domains. Some applications to the existence and regularity of solutions to a homogeneous complex Monge-Ampere equation with prescribed boundary singularity will also be discussed. This is based on my recent work, some of which are joint with Professor Xiaojun Huang.