This paper discusses the properties of the inner puffed-up rim that forms in circumstellar disks when dust evaporates. We argue that the rim shape is controlled by a fundamental property of circumstellar disks, namely their very large vertical density gradient, through the dependence of grain evaporation temperature on gas density. As a result, the bright side of the rim is curved, rather than vertical, as expected when a constant evaporation temperature is assumed. We have computed a number of rim models that take into account this effect in a self-consistent way. The results show that the curved rim (as the vertical rim) emits most of its radiation in the near and mid-IR, and provides a simple explanation for the observed values of the near-IR excess (the “3 μm bump” of Herbig Ae stars). Contrary to the vertical rim, for curved rims the near-IR excess does not depend much on the inclination, being maximum for face-on objects. We then computed synthetic images of the curved rim seen under different inclinations; face-on rims are seen as bright, centrally symmetric rings on the sky; increasing the inclination, the rim takes an elliptical shape, with one side brighter than the other.