2001/12/31 by Michel Rumin · 1 citation
Mathematics · #math.DG #msc:58J50 #msc:58A10 #msc:58J10 #msc:53C17
published as Seminaire de theorie spectrale et geometrie de Grenoble, vol 19 (2001), 123-164 · 36 pages; some typos corrected
arxiv created 2002/05/13 · arxiv updated 2009/11/30
One knows that the large time heat decay exponent on a nilpotent group is given by half the growing rate of the volume of its large balls. This work deals with the similar problem of trying to interpret geometrically the heat decay on (one) forms. We will show how it is (partially) related to the depth of the relations required to define the group. The tools used apply in general on Carnot-Caratheodory manifolds.