CRM: Centro De Giorgi
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Some topics of Geometric Analysis and Geometric Measure Theory

On the Sobolev quotient in sub-Riemannian geometry

speaker: Andrea Malchiodi (Scuola Normale Superiore)

abstract: We consider a class of three-dimensional “CR manifolds” which are modelled on the Heisenberg group. We introduce a natural concept of “mass” and prove its positivity under the conditions that the Webster curvature is positive and in relation to their (holomorphic)embeddability properties. We apply this result to the CR Yamabe problem, and we discuss the properties of Sobolev-type quotients, giving some counterexamples for “Rossi spheres”. This is joint work with J.H.Cheng and P.Yang.

Wed 17 Apr, 9:30 - 10:20, Aula Dini
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