A notion of robustness and stability of manifolds
| dc.WoS.categories | Mathematics, Applied; Mathematics | en_US |
| dc.authorid | 0000-0003-3833-6397 | en_US |
| dc.contributor.author | Deniz, Ali | |
| dc.contributor.author | Koçak, Şahin | |
| dc.contributor.author | Ratiu, Andrei V. | |
| dc.date.accessioned | 2021-01-21T06:13:42Z | |
| dc.date.available | 2021-01-21T06:13:42Z | |
| dc.date.issued | 2008-06-01 | |
| dc.description.abstract | Starting from the notion of thickness of Parks we define a notion of robustness for arbitrary subsets of R-k and we investigate its relationship with the notion of positive reach of Federer. We prove that if a set M is robust, then its boundary a M is of positive reach and conversely (under very mild restrictions) if partial derivative M is of positive reach, then M is robust. We then prove that a closed non-empty robust set in R-k (different from R-k) is a codimension zero submanifold of class C-1 with boundary. As a partial converse we show that any compact codimension zero submanifold with boundary of class C-2 is robust. Using the notion of robustness we prove a kind of stability theorem for codimension zero compact submanifolds with boundary: two such submanifolds, whose boundaries are close enough (in the sense of Hausdorff distance), are diffeomorphic. (C) 2007 Elsevier Inc. All rights reserved. | en_US |
| dc.fullTextLevel | Full Text | en_US |
| dc.identifier.doi | 10.1016/j.jmaa.2007.12.025 | |
| dc.identifier.issn | 0022-247X | |
| dc.identifier.scopus | 2-s2.0-39949084488 | en_US |
| dc.identifier.uri | https://hdl.handle.net/11411/3144 | |
| dc.identifier.uri | https://doi.org/10.1016/j.jmaa.2007.12.025 | |
| dc.identifier.wos | WOS:000254880300044 | en_US |
| dc.identifier.wosquality | Q1 | en_US |
| dc.indekslendigikaynak | Web of Science | en_US |
| dc.indekslendigikaynak | Scopus | en_US |
| dc.issue | 1 | en_US |
| dc.language.iso | en | en_US |
| dc.national | International | en_US |
| dc.numberofauthors | 3 | en_US |
| dc.pages | 524-533 | en_US |
| dc.publisher | Academic Press Inc Elsevier Science | en_US |
| dc.relation.ispartof | Journal Of Mathematical Analysis And Applications | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | thickness | en_US |
| dc.subject | positive reach | en_US |
| dc.subject | stability of manifolds | en_US |
| dc.subject | Hausdortf distance | en_US |
| dc.title | A notion of robustness and stability of manifolds | |
| dc.type | Article | |
| dc.volume | 342 | en_US |
