I expect frying pans with raised ridges are for a few purposes such as adding "grill lines" to meats and keeping food out of grease somewhat as it collects.
Why or when should I use a frying pan with raised ridges?
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If you roast e.g. slices of eggplant in your grill pan, you need substantially less fat than if you roast it in a flat-bottomed pan: you only need to lightly brush the eggplant with a tiny bit. (So far this is experience, from now on educated guessing and basic physics :) ) I would think this is because you can keep the grill pan at a bit higher heat: there is less contact area with the food, and contact with food cools the pan down, because the food is a lot colder than the pan itself. This means that the smaller contact area itself is heated more intensely and crisps to the beautiful and flavourful black lines (which are also somewhat non-stick!) while retaining just enough structural integrity to be able to turn the slice over and remove it from the pan. If you would superheat a flat-bottomed pan to the temperature you would need to achieve the same effect on the whole face of the eggplant slice, it would have to be quite a bit hotter, your eggplant would be completely blackened, and it wouldn't have as much structural integrity left.
The same is true for most vegetables that have the same sort of consistency and water content: bell peppers, mushrooms, zucchini, ... With meat, I think the same is true, but to a somewhat lesser extent, due to the higher density of meat. With thinner strips though, you can get the same effect.