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<p>Given a strictly pseudoconvex CR manifold <i>M</i> of dimension three and positive CR Yamabe class, and a positive smooth function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(K:M\rightarrow \textbf{R}\)</EquationSource> </InlineEquation> verifying some mild and generic hypotheses, we prove the compactness of the set of solutions of the Webster curvature prescription problem associated to <i>K</i>, and we compute the Leray-Schauder degree in terms of the critical points of <i>K</i>. As a corollary, we get an existence result which generalizes the ones existent in the literature.</p>

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

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  • 发表日期：

    2025年9月17日

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  • Claudio Afeltra

摘要

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.