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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2204.10449 |
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| _version_ | 1866914863405596672 |
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| author | Miura, Tatsuya Tanaka, Minoru |
| author_facet | Miura, Tatsuya Tanaka, Minoru |
| contents | For the distance function from any closed subset of any complete Finsler manifold, we prove that the singular set is equal to a countable union of delta-convex hypersurfaces up to an exceptional set of codimension two. In addition, in dimension two, the whole singular set is equal to a countable union of delta-convex Jordan arcs up to isolated points. These results are new even in the standard Euclidean space and shown to be optimal in view of regularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_10449 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Delta-convex structure of the singular set of distance functions Miura, Tatsuya Tanaka, Minoru Analysis of PDEs Differential Geometry 49J52, 53C22, 53C60, 49L25, 35F21 For the distance function from any closed subset of any complete Finsler manifold, we prove that the singular set is equal to a countable union of delta-convex hypersurfaces up to an exceptional set of codimension two. In addition, in dimension two, the whole singular set is equal to a countable union of delta-convex Jordan arcs up to isolated points. These results are new even in the standard Euclidean space and shown to be optimal in view of regularity. |
| title | Delta-convex structure of the singular set of distance functions |
| topic | Analysis of PDEs Differential Geometry 49J52, 53C22, 53C60, 49L25, 35F21 |
| url | https://arxiv.org/abs/2204.10449 |