A Frobenius Theorem for Corank-1 Continuous Distributions in Dimensions two and three
classification
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math.APmath.DS
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theoremcontinuouscorank-1dimensionsdistributionsfrobeniusthreeasymptotic
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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.
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