Blow-up analysis and degree theory for the Webster curvature prescription problem in three dimensions

2024/09/11 by Claudio Afeltra, Afeltra, Claudio
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2409.07334

openalex publication_date 2024/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

Given a strictly pseudoconvex CR manifold M of dimension three and positive CR Yamabe class, and a positive smooth function K:M\toR 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.

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