Homological Filling and Minimal Varifolds in Four-Dimensional Einstein Manifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912946927435776 |
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| author | Fu, Wenjie Zhu, Zhifei |
| author_facet | Fu, Wenjie Zhu, Zhifei |
| contents | We study the smallest area $A(M,g)$ of a 2-dimensional stationary integral varifold in a closed Einstein 4-manifold $(M^4,g)$ with $Ric_g = λg, |λ|\leq 3, Vol(M,g)\geq v>0, diam(M,g)\leq D, H_1(M;\mathbb{Z})=0.$ Building on the previous work on homological filling functions, we show that for every $(M^4,g)$ in this Einstein class, there is an upper bound $A(M,g)\leq F_{Ein}(v,D),$ where $F_{Ein}$ depends only on $(v,D)$ and on quantitative Sobolev and $\varepsilon$-regularity constants for Einstein metrics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14016 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homological Filling and Minimal Varifolds in Four-Dimensional Einstein Manifolds Fu, Wenjie Zhu, Zhifei Differential Geometry 53C23 We study the smallest area $A(M,g)$ of a 2-dimensional stationary integral varifold in a closed Einstein 4-manifold $(M^4,g)$ with $Ric_g = λg, |λ|\leq 3, Vol(M,g)\geq v>0, diam(M,g)\leq D, H_1(M;\mathbb{Z})=0.$ Building on the previous work on homological filling functions, we show that for every $(M^4,g)$ in this Einstein class, there is an upper bound $A(M,g)\leq F_{Ein}(v,D),$ where $F_{Ein}$ depends only on $(v,D)$ and on quantitative Sobolev and $\varepsilon$-regularity constants for Einstein metrics. |
| title | Homological Filling and Minimal Varifolds in Four-Dimensional Einstein Manifolds |
| topic | Differential Geometry 53C23 |
| url | https://arxiv.org/abs/2512.14016 |