This is relate to How to move a Tumblr blog without hurting PageRank? question.
I used custom domain for Tumblr for about a week, some of Tumblr domain disappeared and most of the posts appeared in new domain in search results.
After that, I moved my files to my new host, and pointed my domain name there, hoping that Tumblr won't notice the change and keep redirecting users to my domain.
Unfortunately, Tumblr realized (after 2 days) that I don't point to their servers anymore, and stopped redirecting to my domain.
Does having old blog running hurt my search results rankings because of duplicate content? If so, I want to close my Tumblr blog. On the other hand, I am considering that some people might lose track of my blog. So I am confused. What is the optimal thing to do here, close old blog or not?
Edit: I am also considering changing all posts to mere links to new content in old blog. Is it a good idea?