Selling A House Co-owned With An Ex

I co-own a house in Georgia with an ex. We are both on the deed as joint tenants. I am the only one on the mortgage. We also currently have a HELOC with a balance.

After the breakup they elected to remain in the house and we had an agreement they’d pay the entire mortgage for a year. That year is coming up and they indicated they’re buying a new home and moving out. They’ve given multiple indications that they don’t intend to contribute to the mortgage afterwards.

On top of that, they asked me to provide their lender for their upcoming purchase with a year of bank statements showing I was solely responsible for paying for the mortgage, HELOC, taxes, insurance. This to me appears fraudulent, as they were paying me for those costs. IIRC they stated on the phone that they need it to show release from liability on the house we co-own. I have not provided these statements.

Do I have any legal recourse if they don’t contribute after they move out and the house is vacant? I’m guessing the HELOC now ties them financially to the home, but that may be only for the amount of the HELOC balance.