If you can slightly lift where they are coming up you can use tile mastic and stick them back down. You can also use 3M Super 77 spray adhesive under the curls. Normally cork tiles are glued down with rubber contact cement.
Due to dropping various things on the ceramic tile floor in my kitchen, I have quite a few small nicks and one larger one - want to find something to cover them up, c...
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If you can slightly lift where they are coming up you can use tile mastic and stick them back down. You can also use 3M Super 77 spray adhesive under the curls. Normally cork tiles are glued down with rubber contact cement.
I agree with William, you should be able to stick those corners back down.
After you add extra adhesive place something very heavy on them to keep it flat for a few days
Here's an article I found that will help:
http://corkfloor.us/cork-floor-care.html
Are they curling due to moisture? Cork does not tolerate wet conditions.