I want to put the blog_signup_form directly on the profile page if the user hasn’t registered a blog yet. That is relatively easy to do, but it then shows up on other users’ profiles as well -> it should only show up on the user’s own profile.

Is there a check like if ( is_my_profile() ) ?

Something with function bp_loggedin_user_id perhaps, like if (bp_loggedin_user_id()) = profile_id ?

Edit:

This seems to do the trick:

[@r-a-y Keymaster 15 years, 3 months ago]

If you’re using BP 1.2, try:
bp_is_my_profile()

This doesn’t exist in the BP 1.1 series (which I’m guessing you’re still using), so here’s the complete function that you can plop into your theme’s functions.php:
http://pastebin.com/nfm8WFVf