Coercive Inequalities on Carnot Groups: Taming Singularities

In the setting of Carnot groups, we propose an approach of taming singularities to get coercive inequalities. That is, we develop a technique to introduce natural singularities in the energy function U in order to force one of the coercivity conditions. In particular, we explore explicit constructions of probability measures on Carnot groups which secure Poincaré and even Logarithmic Sobolev inequalities.

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