A new conformal heat flow of harmonic maps
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913379063431168 |
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| author | Park, Woongbae |
| author_facet | Park, Woongbae |
| contents | We introduce and study a conformal heat flow of harmonic maps defined by an evolution equation for a pair consisting of a map and a conformal factor of metric on the two-dimensional domain. This flow is designed to postpone finite time singularity but does not get rid of possibility of bubble forming. We show that Struwe type global weak solution exists, which is smooth except at most finitely many points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_05978 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A new conformal heat flow of harmonic maps Park, Woongbae Differential Geometry Analysis of PDEs Primary 58E20, 53E99, 53C43, Secondary 35K58 We introduce and study a conformal heat flow of harmonic maps defined by an evolution equation for a pair consisting of a map and a conformal factor of metric on the two-dimensional domain. This flow is designed to postpone finite time singularity but does not get rid of possibility of bubble forming. We show that Struwe type global weak solution exists, which is smooth except at most finitely many points. |
| title | A new conformal heat flow of harmonic maps |
| topic | Differential Geometry Analysis of PDEs Primary 58E20, 53E99, 53C43, Secondary 35K58 |
| url | https://arxiv.org/abs/2202.05978 |