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https://hdl.handle.net/2440/120070
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dc.contributor.author | Forstneric, F. | - |
dc.contributor.author | Larusson, F. | - |
dc.date.issued | 2019 | - |
dc.identifier.citation | Communications in Analysis and Geometry, 2019; 27(1):1-45 | - |
dc.identifier.issn | 1019-8385 | - |
dc.identifier.issn | 1944-9992 | - |
dc.identifier.uri | http://hdl.handle.net/2440/120070 | - |
dc.description.abstract | Let M be an open Riemann surface. It was proved by Alarcón and Forstnerič (arXiv:1408.5315) that every conformal minimal immersion M→R3 is isotopic to the real part of a holomorphic null curve M→C3. In this paper, we prove the following much stronger result in this direction: for any n≥3, the inclusion ι of the space of real parts of nonflat null holomorphic immersions M→Cn into the space of nonflat conformal minimal immersions M→Rn satisfies the parametric h-principle with approximation; in particular, it is a weak homotopy equivalence. We prove analogous results for several other related maps, and we describe the homotopy type of the space of all holomorphic immersions M→Cn. For an open Riemann surface M of finite topological type, we obtain optimal results by showing that ι and several related maps are inclusions of strong deformation retracts; in particular, they are homotopy equivalences. | - |
dc.description.statementofresponsibility | Franc Forstneric, Finnur Larusson | - |
dc.language.iso | en | - |
dc.publisher | International Press | - |
dc.rights | Copyright status unknown | - |
dc.source.uri | http://apps.webofknowledge.com/InboundService.do?customersID=LinksAMR&mode=FullRecord&IsProductCode=Yes&product=WOS&Init=Yes&Func=Frame&DestFail=http://www.webofknowledge.com&action=retrieve&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&SID=E39OiKrtTw5zSGHRSOY&UT=WOS:000467043400001 | - |
dc.subject | Mathematics | - |
dc.title | The parametric h-principle for minimal surfaces in Rⁿ and null curves in Cⁿ | - |
dc.title.alternative | The parametric h-principle for minimal surfaces in R(n) and null curves in C(n) | - |
dc.type | Journal article | - |
dc.identifier.doi | 10.4310/cag.2019.v27.n1.a1 | - |
dc.relation.grant | http://purl.org/au-research/grants/arc/DP150103442 | - |
pubs.publication-status | Published | - |
dc.identifier.orcid | Larusson, F. [0000-0001-5691-4942] | - |
Appears in Collections: | Aurora harvest 4 Mathematical Sciences publications |
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