Around heat decay on forms and relations of nilpotent Lie groups

By M. Rumin. 2001

54 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/16cff54070d4a750f361feed6b07bc87bb9d40c4

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Compensated compactness for differential forms in Carnot groups and applications (2010, methodology): “Rumin in [25] and [24] ([23] for contact structures), so that we are provided with a good setting for our theory.”
Limiting Bourgain–Brezis estimates for systems of linear differential equations: Theme and variations (2014, methodology): “This result was used to obtain the Gagliardo–Nirenberg inequality for forms in the Rumin complex [78, 79, 80, 81] and for forms on the Heisenberg groups H(1) and H(2) [10].”
Riesz transform on manifolds and heat kernel regularity (2004, background): “It would certainly be interesting to investigate the class of manifolds where this domination condition holds; unfortunately, this is in general too strong a requirement, since for instance it does not hold for nilpotent Lie groups, as is shown in [80,81], whereas on such groups the Riesz transforms”