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<p>We prove a compactness result for capillary hypersurfaces with mean curvature prescribed by ambient functions, which generalizes the results of Schätzle [<CitationRef CitationID="CR17">17</CitationRef>] and Bellettini [<CitationRef CitationID="CR4">4</CitationRef>] to the capillary case. The proof relies on extending the definition of (unoriented) curvature varifolds with capillary boundary introduced by Wang-Zhang [<CitationRef CitationID="CR19">19</CitationRef>] to the context of oriented integral varifolds. We also discuss the case when the mean curvature of the boundary is prescribed.</p>

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Compactness of capillary hypersurfaces with mean curvature prescribed by ambient functions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月14日

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  • Xuwen Zhang

摘要

We prove a compactness result for capillary hypersurfaces with mean curvature prescribed by ambient functions, which generalizes the results of Schätzle [17] and Bellettini [4] to the capillary case. The proof relies on extending the definition of (unoriented) curvature varifolds with capillary boundary introduced by Wang-Zhang [19] to the context of oriented integral varifolds. We also discuss the case when the mean curvature of the boundary is prescribed.