Stable foliations with respect to Fuglede modulus and level sets of p--harmonic functions

Original · EN

We continue the study of the variation of the p--modulus of a foliation initiated by the first author. We derive the formula for the second variation which allows to study p--stable foliations. We obtain some results concerning codimension one p--stable foliations. Moreover, we derive the equation for the critical point of the p--modulus functional of a foliation given by the level sets of smooth function. We show the correlation with the q--harmonicity. We give some examples. In particular, we show that foliations given by the distance function are critical points of p--modulus functional.