High-resolution altimetry collected by the Magellan spacecraft reveals trench and outer rise topographic signatures around major coronae (e.g. Eithinoha, Heng-O, Artemis, and Latona). In addition, Magellan synthetic aperature radar images show circumferential fractures in areas where the plates are curved downward. Both observations suggest that the lithosphere around coronae is flexed downward by the weight of the overriding coronal rim or by the negative buoyancy of subducted lithosphere. We have modelled the trench and outer rise topography as a thin elastic plate subjected to a line load and bending moment beneath the corona rim. The approach was tested at northern Freyja Montes where the best fit elastic thickness is 18 km, in agreement with previously published results. The elastic thicknesses determined by modelling numerous profiles at Eithinoha, Heng-O, Artemis, and Latona are 15, 40, 37, and 35 km, respectively. At Eithinoha, Artemis, and Latona where the plates appear to be yielding, the maximum bending moments and elastic thicknesses are similar to those found at the Middle America, Mariana, and Aleutian trenches on Earth, respectively. Estimates of effective elastic thickness and plate curvature are used with a yield strength envelope model of the lithosphere to estimate lithospheric temperature gradients. At Heng-O, Artemis, and Latona, temperature gradients are less than 10 K/km, which correspond to conductive heat losses of less than one half the expected average planetary value. We propose two scenarios for the creation of the ridge, trench, and outer rise topography: differential thermal subsidence and lithospheric subduction. The topography of Heng-O is well matched by the differential thermal subsidence model. However, at Artemis and Latona the amplitudes of the trench and outer rise signatures are a factor of 5 too large to be explained by thermal subsidence alone. In these cases we favor the lithospheric subduction model wherein the lithosphere outboard of the corona perimeter subducts (rolls back) and the corona diameter increases.