Lipid domains less than 200 nm in size may form a scaffold, enabling the concerted function of plasma membrane proteins. The size-regulating mechanism is under debate. We tested the hypotheses that large values of spontaneous monolayer curvature are incompatible with micrometer-sized domains. Here, we used the transition of photoswitchable lipids from their cylindrical conformation to a conical conformation to increase the negative curvature of a bilayer-forming lipid mixture. In contrast to the hypothesis, pre-existing micrometer-sized domains did not dissipate in our planar bilayers, as indicated by fluorescence images and domain mobility measurements. Elasticity theory supports the observation by predicting the zero free energy gain for splitting large domains into smaller ones. It also indicates an alternative size-determining mechanism: The cone-shaped photolipids reduce the line tension associated with lipid deformations at the phase boundary and thus slow down the kinetics of domain fusion. The competing influence of two approaching domains on the deformation of the intervening lipids is responsible for the kinetic fusion trap. Our experiments indicate that the resulting local energy barrier may restrict the domain size in a dynamic system.