THREE-SPHERES THEOREMS FOR SUBELLIPTIC QUASILINEAR EQUATIONS IN CARNOT GROUPS OF HEISENBERG-TYPE

摘要

We study the arithmetic three-spheres theorems for subsolutions of subelliptic PDEs of p-harmonic type in Carnot groups of Heisenberg type for 1 < p < infinity. In the presentation we exhibit the special cases of sub-Laplace equations (p = 2) and the case p is equal to the homogeneous dimension of a Carnot group. Corollaries include asymptotic behavior of subsolutions for small and large radii and the Liouville-type theorems.