Blow-up analysis and degree theory for the Webster curvature prescription problem in three dimensions
Claudio Afeltra · Calculus of Variations and Partial Differential Equations · 2025
Abstract Given a strictly pseudoconvex CR manifold M of dimension three and positive CR Yamabe class, and a positive smooth function $$K:M\rightarrow \textbf{R}$$ verifying some mild and generic hypotheses, we prove the compactness of the set of solutions of the Webster curvature prescription problem associated to K , and we compute the Leray-Schauder degree in terms of the critical points of K . As a corollary, we get an existence result which generalizes the ones existent in the literature.