Sala Seminari (Dip. Matematica).<\/p>\n
In Heisenberg groups, and, more in general, in Carnot groups, equipped with their Carnot- Carathodory metric, the analogous of regular (Euclidean) surfaces of low co-dimensionkcan be consideredG-regular surfaces (H-regular ifG=Hn), i.e. level sets of continuously Pansu- differentiable functionsf:G\u2212\u2192Rkwhose differential is subjective. If it is possible to split the groupGin the product of two suitable homogeneous complementary subgroupsMandH, aG-regular surfaces can be locally seen as anuniformly intrinsic differentiable graphs, defined by a unique continuous function\u03c6acting betweenMandH. Moreover, it turns out that any one co-dimensionalH-regular surface locally defines an implicit function\u03c6, which is of classC1with respect to a suitable non linear vector field\u2207\u03c6expressed in terms of the function\u03c6itself. We extend some of these results characterizing uniformly intrinsic differentiable functions\u03c6acting between two complementary subgroups with target space horizontal of dimensionk, with 1\u2264k\u2264n, in terms of the Euclidean regularity of its components with respect to a family of non linear vector fields{\u2207\u03c6j}j=1,…,k. Eventually, we show how the area of the intrinsic graph of\u03c6can be computed through the component of the matrix identifying the intrinsic differential of\u03c6. <\/p>\n","protected":false},"excerpt":{"rendered":"
In Heisenberg groups, and, more in general, in Carnot groups, equipped with their Carnot- Carathodory metric, the analogous of regular (Euclidean) surfaces of low co-dimensionkcan be consideredG-regular surfaces (H-regular ifG=Hn), i.e. level sets…<\/p>\n