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Files can be opened directly from Dropbox or any other file manager. At the moment, it is only possible to open files read only. Editing mind maps is not yet possible.
The application is in a very early state right now. Please send me an email to email@example.com if you have wishes, suggestions and feedback. Thanks!
 FreePlane: http://freeplane.sourceforge.net/wiki/index.php/Main_Page
 FreeMind: http://freemind.sourceforge.net/wiki/index.php/Main_Page