Unique jet determination of CR maps into Nash sets
<p dir="ltr">Let M ⊂ C<sup>N</sup> be a real-analytic CR submanifold, M′ ⊂ C<sup>N′ </sup>a Nash set and <sup>E</sup>M′ the set of points in M′ of D'Angelo infinite type. We show that if M is minimal, then, for every point p ∈ M , and for ever...
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2023
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| _version_ | 1864513530431012864 |
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| author | Bernhard Lamel (14152263) |
| author2 | Nordine Mir (14158962) Guillaume Rond (17807399) |
| author2_role | author author |
| author_facet | Bernhard Lamel (14152263) Nordine Mir (14158962) Guillaume Rond (17807399) |
| author_role | author |
| dc.creator.none.fl_str_mv | Bernhard Lamel (14152263) Nordine Mir (14158962) Guillaume Rond (17807399) |
| dc.date.none.fl_str_mv | 2023-11-01T00:00:00Z |
| dc.identifier.none.fl_str_mv | 10.1016/j.aim.2023.109271 |
| dc.relation.none.fl_str_mv | https://figshare.com/articles/journal_contribution/Unique_jet_determination_of_CR_maps_into_Nash_sets/25018016 |
| dc.rights.none.fl_str_mv | CC BY 4.0 info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Mathematical sciences Pure mathematics CR maps Finite jet determination |
| dc.title.none.fl_str_mv | Unique jet determination of CR maps into Nash sets |
| dc.type.none.fl_str_mv | Text Journal contribution info:eu-repo/semantics/publishedVersion text contribution to journal |
| description | <p dir="ltr">Let M ⊂ C<sup>N</sup> be a real-analytic CR submanifold, M′ ⊂ C<sup>N′ </sup>a Nash set and <sup>E</sup>M′ the set of points in M′ of D'Angelo infinite type. We show that if M is minimal, then, for every point p ∈ M , and for every pair of germs of C<sup>∞</sup> -smooth CR maps f , g : ( M , p ) → M′ , there exists an integer k = k<sub>p</sub> such that if f and g have the same k-jets at p, and do not send M into E M′ , then necessarily f = g . Furthermore, the map p ↦ k p may be chosen to be bounded on compact subsets of M. As a consequence, we derive the finite jet determination property for pairs of germs of CR maps from minimal real-analytic CR submanifolds in C <sup>N</sup> into Nash subsets in C<sup>N′ </sup>of D'Angelo finite type, for arbitrary N , N′ ≥ 2.</p><h2>Other Information</h2><p dir="ltr">Published in: Advances in Mathematics<br>License: <a href="http://creativecommons.org/licenses/by/4.0/" target="_blank">http://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1016/j.aim.2023.109271" target="_blank">https://dx.doi.org/10.1016/j.aim.2023.109271</a></p> |
| eu_rights_str_mv | openAccess |
| id | Manara2_3e534a263aef081b9f856c5602539d90 |
| identifier_str_mv | 10.1016/j.aim.2023.109271 |
| network_acronym_str | Manara2 |
| network_name_str | Manara2 |
| oai_identifier_str | oai:figshare.com:article/25018016 |
| publishDate | 2023 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | CC BY 4.0 |
| spelling | Unique jet determination of CR maps into Nash setsBernhard Lamel (14152263)Nordine Mir (14158962)Guillaume Rond (17807399)Mathematical sciencesPure mathematicsCR mapsFinite jet determination<p dir="ltr">Let M ⊂ C<sup>N</sup> be a real-analytic CR submanifold, M′ ⊂ C<sup>N′ </sup>a Nash set and <sup>E</sup>M′ the set of points in M′ of D'Angelo infinite type. We show that if M is minimal, then, for every point p ∈ M , and for every pair of germs of C<sup>∞</sup> -smooth CR maps f , g : ( M , p ) → M′ , there exists an integer k = k<sub>p</sub> such that if f and g have the same k-jets at p, and do not send M into E M′ , then necessarily f = g . Furthermore, the map p ↦ k p may be chosen to be bounded on compact subsets of M. As a consequence, we derive the finite jet determination property for pairs of germs of CR maps from minimal real-analytic CR submanifolds in C <sup>N</sup> into Nash subsets in C<sup>N′ </sup>of D'Angelo finite type, for arbitrary N , N′ ≥ 2.</p><h2>Other Information</h2><p dir="ltr">Published in: Advances in Mathematics<br>License: <a href="http://creativecommons.org/licenses/by/4.0/" target="_blank">http://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1016/j.aim.2023.109271" target="_blank">https://dx.doi.org/10.1016/j.aim.2023.109271</a></p>2023-11-01T00:00:00ZTextJournal contributioninfo:eu-repo/semantics/publishedVersiontextcontribution to journal10.1016/j.aim.2023.109271https://figshare.com/articles/journal_contribution/Unique_jet_determination_of_CR_maps_into_Nash_sets/25018016CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/250180162023-11-01T00:00:00Z |
| spellingShingle | Unique jet determination of CR maps into Nash sets Bernhard Lamel (14152263) Mathematical sciences Pure mathematics CR maps Finite jet determination |
| status_str | publishedVersion |
| title | Unique jet determination of CR maps into Nash sets |
| title_full | Unique jet determination of CR maps into Nash sets |
| title_fullStr | Unique jet determination of CR maps into Nash sets |
| title_full_unstemmed | Unique jet determination of CR maps into Nash sets |
| title_short | Unique jet determination of CR maps into Nash sets |
| title_sort | Unique jet determination of CR maps into Nash sets |
| topic | Mathematical sciences Pure mathematics CR maps Finite jet determination |