Memoirs of a Geisha Font

Memoirs of a Geisha is a 2005 movie adaptation of the novel of the same name by Arthur Golden. The film tells the story of a young girl named Chiyo who is sold into servitude and eventually becomes a geisha in pre-World War II Japan.

The movie title in the poster is probably set in a font called Trajan by Carol Twombly. This is a commercial font and you can find additional information about it here.