Yes, there is an app for that. It's called "AllShare" and it should be pre-installed on Your Galaxy. It uses a protocol called DLNA (Digital Living Network Alliance.)
http/www.dlna.org/
Now, to figure out if You have the receiver built into Your "Sony Home Theater"...I don't know...maybe Google knows: https/www.google.com/search?q=sony+dlna
If DLNA is not built into Your existing setup, jonny_street is right, and a ChromeCast Dongle would add a DLNA receiver to an open HDMI port.