In biology, epithelial morphogenesis of thin sheet-like structures in plants and animals is responsible for the vast majority of functional structures that make up organs and organisms. These may be modeled effectively as two-dimensional surfaces whose geometry is driven by active processes that are intimately connected to the presence of orientational order in the tangent plane that modifies the embedding and in turn is modified by it. The nature of in-plane order is akin to that of polar molecules, liquid crystals, etc., or more generally to p-fold rotational order, denoted as ‘‘p-atics’’.1 There is a growing body of evidence suggesting that topological defects, singular disruptions of the rotational order, play a crucial role in guiding or controlling morphogenesis, as seen in experimental observations of cell extrusion and apoptosis,2 mound formation,3,4 layer formation,5 and body shaping using bulges, pits and tentacles.6 These observations suggest a natural question: how might one construct a theoretical framework that accounts for the dynamics of topological defects on non-uniform surfaces which themselves deform in response to the forces induced by the defects?