A Frobenius theorem for corank-1 continuous distributions in dimensions two and three

作者：Luzzatto S^*; Tureli S; War K M

来源：International Journal of Mathematics, 2016, 27(8): 1650061.

DOI：10.1142/S0129167X16500610

• Frobenius theorem
• continuous tangent sub-bundles
• integrability
• ordinary differential equations
• partial differential equations

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 Frobenius theorem, which says that an involutive C-1 distribution is uniquely integrable.

• 出版日期2016-7