Almost minimizing Yang$-$Mills fields: log-epiperimetric inequality, non-concentration, and uniqueness of tangents
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910702201995264 |
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| author | Caniato, Riccardo Parise, Davide |
| author_facet | Caniato, Riccardo Parise, Davide |
| contents | We establish a direct log-epiperimetric inequality for Yang$-$Mills fields in arbitrary dimension and we leverage on it to prove uniqueness of tangent cones with isolated singularity for energy minimizing Yang$-$Mills fields and $ω$-ASD connections (where $ω$ is not necessarily closed) satisfying some suitable regularity assumptions. En route to this we establish a Luckhaus type lemma for Yang$-$Mills connections to exclude curvature concentration along blow-up sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15540 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Almost minimizing Yang$-$Mills fields: log-epiperimetric inequality, non-concentration, and uniqueness of tangents Caniato, Riccardo Parise, Davide Differential Geometry Analysis of PDEs Functional Analysis 58E15 (primary), 53C07 We establish a direct log-epiperimetric inequality for Yang$-$Mills fields in arbitrary dimension and we leverage on it to prove uniqueness of tangent cones with isolated singularity for energy minimizing Yang$-$Mills fields and $ω$-ASD connections (where $ω$ is not necessarily closed) satisfying some suitable regularity assumptions. En route to this we establish a Luckhaus type lemma for Yang$-$Mills connections to exclude curvature concentration along blow-up sequences. |
| title | Almost minimizing Yang$-$Mills fields: log-epiperimetric inequality, non-concentration, and uniqueness of tangents |
| topic | Differential Geometry Analysis of PDEs Functional Analysis 58E15 (primary), 53C07 |
| url | https://arxiv.org/abs/2410.15540 |