6 papers
A non-convergence phenomenon for the CR Yamabe flow
Claudio Afeltra, Andrea Pinamonti, Pak Tung Ho
We construct a contact form on a three dimensional CR manifold such that the CR Yamabe flow fails to converge. More precisely, on small Rossi deformations of the standard CR three-…
Compactness in Dimension Five and Equivariant Noncompactness for the CR Yamabe Problem
Claudio Afeltra, Andrea Pinamonti, Pak Tung Ho
We study compactness and noncompactness phenomena for the CR Yamabe equation on compact strictly pseudoconvex CR manifolds. First, in dimension five we establish uniform \emph{a pr…
A CR structure with blowing up solutions to the CR Yamabe problem
Claudio Afeltra, Andrea Pinamonti
We prove the existence of a CR structure on such that the set of solutions to the CR Yamabe problem is not compact and admits a blowing-up sequence. Such CR structure is buil…
Blow-up analysis and degree theory for the Webster curvature prescription problem in three dimensions
Claudio Afeltra
Given a strictly pseudoconvex CR manifold of dimension three and positive CR Yamabe class, and a positive smooth function verifying some mild and generic hyp…
A compactness result for the CR Yamabe problem in three dimensions
Claudio Afeltra
We prove the compactness of the set of solutions to the CR Yamabe problem on a compact strictly pseudoconvex CR manifold of dimension three whose blow-up manifolds at every point h…
Singular solutions of the Yamabe problem in the Heisenberg group and their bifurcation
Claudio Afeltra
We prove the existence of a homogeneous singular solution of the critical equation on the Heisenberg group , where is the \textit{homogeneous…