Bricks, Masonry, Asphalt and Concrete - Sloping Concrete Porch

We just bought a 2-year old house. It has a nice covered concrete porch that, alas, slopes a little in a couple of places towards the house. There is also some ponding in these places when wind-driven rain or snow that melts gets in there. Water and wood cannot be a good long-term thing. Would anybody have any suggestions? I am thinking maybe a cut in the concrete near the sill the length of the porch (40'?) to allow the water to drain harmlessly out the sides, but that would introduce freeze-thaw issues, no? (I am in the Northeast).

As I said, the porch is like new. It rests on a deep (according to the previous owner) continuous foundation with stone inside. Thanks.