A Frobenius Theorem for Corank-1 Continuous Distributions in Dimensions   two and three
  We formulate a notion of (uniform) asymptotic involutivity and show that it implies (unique) integrability of corank-1 continuous distributions in dimensions three or less. This generalizes and extends a classical theorem of Frobenius Theorem which says that an involutive C^1 distribution is uniquely integrable. 
Stefano Luzzatto, Sina Tureli, Khadim War
math.DG math.AP math.DS