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"Active nematics" are orientationally ordered but apolar fluids composed ofinteracting constituents individually powered by an internal source of energy.When activity exceeds a system-size dependent threshold, spatially uniformactive apolar fluids undergo a hydrodynamic instability leading to spontaneousmacroscopic fluid flow. Here, we show that a special class of spatiallynon-uniform configurations of such active apolar fluids display laminar (i.e.,time-independent) flow even for arbitrarily small activity. We also show thattwo-dimensional active nematics confined on a surface of non-vanishing Gaussiancurvature must necessarily experience a non-vanishing active force. Thisgeneral conclusion follows from a key result of differential geometry:geodesics must converge or diverge on surfaces with non-zero Gaussiancurvature. We derive the conditions under which such curvature-induced activeforces generate "thresholdless flow" for two-dimensional curved shells. We thenextend our analysis to bulk systems and show how to induce thresholdless activeflow by controlling the curvature of confining surfaces, external fields, orboth. The resulting laminar flow fields are determined analytically in threeexperimentally realizable configurations that exemplify this generalphenomenon: i) toroidal shells with planar alignment, ii) a cylinder withnon-planar boundary conditions, and iii) a "Frederiks cell" that functions likea pump without moving parts. Our work suggests a robust design strategy foractive microfluidic chips and could be tested with the recently discovered"living liquid crystals".

The geometry of thresholdless active flow in nematic microfluidics