For cells to divide or branch, they need to be able to sense their own shape, localizing proteins to regions of high or low curvature. Curved proteins prefer to bind to curved membranes, which can explain some of this shape sensitivity. However, when the membrane has curvature on the micron scale, and proteins are on the nanometer scale, single-protein sensing may be challenging. Shape sensing can also arise from the collective action of many proteins even if single proteins don’t sense curvature - i.e. the shape sensing is emergent. In particular, it is known that the motion of traveling waves arising from reaction-diffusion processes on a curved surface is altered by surface curvature. Common biochemical reactions that distinguish the cell front from rear (Rho GTPase polarity, modeled by a “wave-pinning” mechanism) also sense shape, with the cell front pointing toward the narrow end of an elongated cell. However, it is not completely clear what aspects of the cell geometry the wave-pinning reaction senses. Does the cell front localize to high mean or Gaussian curvature, or a different shape feature altogether? Is this shape sensing disrupted by the membrane fluctuations? We address these questions with a combination of detailed simulation of reaction-diffusion on a curved membrane surface and a phenomenological theory that allows us to construct an energy landscape to predict where these domains localize. This landscape theory allows us to develop a coarse-grained model of how regions of high Rho signaling will diffuse on a fluctuating membrane.