52 citations · 103 across the 8 of their papers we have counts for
9 papers
Topological and dynamical aspects of some spectral invariants of contact manifolds with circle action
Michel Rumin
We study analytic torsion and eta like invariants on CR contact manifolds of any dimension admitting a circle transverse action, and equipped with a unitary representation. We show…
On the l^{q,p} cohomology of Carnot groups
Pierre Pansu, Michel Rumin
We study the simplicial {\ell} q,p cohomology of Carnot groups G. We show vanishing and non-vanishing results depending of the range of the (p, q) gap with respect to the weight ga…
An entropic uncertainty principle for positive operator valued measures
Michel Rumin
Extending a recent result by Frank and Lieb, we show an entropic uncertainty principle for mixed states in a Hilbert space relatively to pairs of positive operator valued measures…
Balanced distribution-energy inequalities and related entropy bounds
Michel Rumin
Let be a self-adjoint operator acting over a space endowed with a partition. We give lower bounds on the energy of a mixed state from its distribution in the partition…
Spectral density and Sobolev inequalities for pure and mixed states
Michel Rumin
We prove some general Sobolev-type and related inequalities for positive operators A of given ultracontractive spectral decay, without assuming e^{-tA} is submarkovian. These inequ…
Around a Sobolev-Orlicz inequality for operators of given spectral density
Michel Rumin
We prove some general Sobolev-Orlicz, Nash and Faber-Krahn inequalities for positive operators of given ultracontractive norms of the spectral projectors on ]0, lambda]. For invari…
Analytic torsions on contact manifolds
Michel Rumin, Neil Seshadri
We propose a definition for analytic torsion of the contact complex on contact manifolds. We show it coincides with Ray-Singer torsion on any 3-dimensional CR Seifert manifold equi…
Diabatic Limit, Eta Invariants and Cauchy-Riemann Manifolds of Dimension 3
Olivier Biquard, Marc Herzlich, Michel Rumin
We relate a recently introduced non-local geometric invariant of compact strictly pseudoconvex Cauchy-Riemann (CR) manifolds of dimension 3 to various eta-invariants in CR geometry…
Around heat decay on forms and relations of nilpotent Lie groups
Michel Rumin
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…