In both Pokemon Go and the main series Pokemon games, I can use Revives and (various types of) Potions to revive and heal my Pokemon while I'm out in the wild. The main series also has Pokemon Centers, where I can heal all of my Pokemon without using items. However, I haven't seen any in Pokemon Go. Are they only available in denser urban areas? Or are they even available at all? Getting recovery items from spinning gyms is not nearly keeping up with the rate of my Pokemon getting injured/knocked out.
Pokemon Centers do not exist in Pokemon Go. The only way to heal and revive your Pokemon is to use potions and revives.1 However, during John Hanke's interview at the 2016 San Diego Comic-Con, he hinted towards similar functionality could come in the future. Given that some features that weren't in the game at initial launch (such as trading and battling) are now in the game, Pokemon Center-like features might happen, but it is merely speculation at this point.
1 There are some less effective ways to revive. If your Pokemon is knocked out, but have stardust and candy to spare, powering up will technically revive them if their base HP increases. This method won't work if the base HP stat doesn't increase or the Pokemon is already level 40