If the corners of the rug are curling curl them backward flatten them back out and place weights in just the corners of the rug.
How to get a kink out of a rug.
Use a drapery steamer.
Place a piece of furniture or a stack of heavy books on the creases for a few days to flatten them out using weight.
I cured this by using a staple gun the pile is so deep you cant see i have stapled the rugs down.
I used to always trip over the rugs in my front room i have a runner over the carpet to the kitchen and one as you walk in.
This should fix your problem immediately.
If you pull it taught while you do this it will get rid of any kinks and makes them a lot easier to hoover.
You may have to do it on the back to get the kinks out and then on the face yarns to get them to settle in with the rest.
Step 4 if your rug still won t lie flat apply some heat to it.