The generalised energy identity and length of necks for $\varepsilon$-harmonic maps
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918450338725888 |
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| author | Roberts, Andrew M. |
| author_facet | Roberts, Andrew M. |
| contents | In this paper we find analogues for $\varepsilon$-harmonic maps to the generalised energy identity and the existence of geodesic necks result discovered by Yuxiang Li and Youde Wang for $α$-harmonic maps. In particular there exist specific quantities depending only on $\varepsilon$ and the bubbling radius which entirely determine if the full energy identity holds and if a neck forms. In the case these fail we can calculate the energy lost and the length of the geodesic neck based on only these quantities and the biharmonic energy of the bubble. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10914 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The generalised energy identity and length of necks for $\varepsilon$-harmonic maps Roberts, Andrew M. Differential Geometry Analysis of PDEs 58E20, 53C43 In this paper we find analogues for $\varepsilon$-harmonic maps to the generalised energy identity and the existence of geodesic necks result discovered by Yuxiang Li and Youde Wang for $α$-harmonic maps. In particular there exist specific quantities depending only on $\varepsilon$ and the bubbling radius which entirely determine if the full energy identity holds and if a neck forms. In the case these fail we can calculate the energy lost and the length of the geodesic neck based on only these quantities and the biharmonic energy of the bubble. |
| title | The generalised energy identity and length of necks for $\varepsilon$-harmonic maps |
| topic | Differential Geometry Analysis of PDEs 58E20, 53C43 |
| url | https://arxiv.org/abs/2602.10914 |