Minimal laminations and level sets of 1-harmonic functions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866911965884973056 |
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| author | Backus, Aidan |
| author_facet | Backus, Aidan |
| contents | We collect several results concerning regularity of minimal laminations, and governing the various modes of convergence for sequences of minimal laminations. We then apply this theory to prove that a function has locally least gradient (is $1$-harmonic) iff its level sets are a minimal lamination; this resolves an open problem of Daskalopoulos and Uhlenbeck. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_01541 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Minimal laminations and level sets of 1-harmonic functions Backus, Aidan Analysis of PDEs Differential Geometry 49Q20, 49Q05, 51F30 We collect several results concerning regularity of minimal laminations, and governing the various modes of convergence for sequences of minimal laminations. We then apply this theory to prove that a function has locally least gradient (is $1$-harmonic) iff its level sets are a minimal lamination; this resolves an open problem of Daskalopoulos and Uhlenbeck. |
| title | Minimal laminations and level sets of 1-harmonic functions |
| topic | Analysis of PDEs Differential Geometry 49Q20, 49Q05, 51F30 |
| url | https://arxiv.org/abs/2311.01541 |