Smooth Stable Foliations of Anosov Diffeomorphisms

In this paper, we focus on the rigidity of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:math> -smooth codimension-one stable foliations of Anosov diffeomorphisms. Specifically, we show that if the regularity of these foliations is slightly bigger than 2, then they will have the same smoothness of the diffeomorphisms.