Some results on the $\mathfrak{g}$-stability of surfaces with boundary
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914263674650624 |
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| author | Lee, Sanghun |
| author_facet | Lee, Sanghun |
| contents | In this paper, we investigate the geometric properties associated with the $\mathfrak{g}$-stability of surfaces with boundary whose null expansion satisfies $Θ^{+} = h \geq 0$. First, we show that a $\mathfrak{g}$-stable hypersurface with free boundary admits a metric of positive scalar curvature with minimal boundary under suitable conditions. Second, for $\mathfrak{g}$-stable surfaces with free boundary, we derive an area estimate and determine the topology of the surface. Finally, we extend our free boundary results to the case of capillary boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13077 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Some results on the $\mathfrak{g}$-stability of surfaces with boundary Lee, Sanghun Differential Geometry 53C24, 53C21, 53A10 In this paper, we investigate the geometric properties associated with the $\mathfrak{g}$-stability of surfaces with boundary whose null expansion satisfies $Θ^{+} = h \geq 0$. First, we show that a $\mathfrak{g}$-stable hypersurface with free boundary admits a metric of positive scalar curvature with minimal boundary under suitable conditions. Second, for $\mathfrak{g}$-stable surfaces with free boundary, we derive an area estimate and determine the topology of the surface. Finally, we extend our free boundary results to the case of capillary boundary. |
| title | Some results on the $\mathfrak{g}$-stability of surfaces with boundary |
| topic | Differential Geometry 53C24, 53C21, 53A10 |
| url | https://arxiv.org/abs/2601.13077 |