韦伯斯特曲率三维处方问题的膨胀分析和度理论

Claudio Afeltra
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引用次数: 0

摘要

给定一个三维正CR山贝类的严格伪凸CR流形$M$和一个正光滑函数$K:M\to\mathbf{R}$,我们证明了与$K$相关的韦伯斯特曲率规定问题的解集的紧凑性,并根据$K$的临界点计算了勒雷-肖德尔度。作为一个推论,我们得到了一个存在性结果,它概括了文献中已有的存在性结果。
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Blow-up analysis and degree theory for the Webster curvature prescription problem in three dimensions
Given a strictly pseudoconvex CR manifold $M$ of dimension three and positive CR Yamabe class, and a positive smooth function $K:M\to\mathbf{R}$ 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.
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