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Variational formulas for submanifolds of fixed degree
dc.contributor.author | Citti, Giovanna | |
dc.contributor.author | Giovannardi, Gianmarco | |
dc.contributor.author | Ritoré Cortés, Manuel María | |
dc.date.accessioned | 2021-09-07T09:52:20Z | |
dc.date.available | 2021-09-07T09:52:20Z | |
dc.date.issued | 2021 | |
dc.identifier.citation | Citti, G., Giovannardi, G. & Ritoré, M. Variational formulas for submanifolds of fixed degree. Calc. Var. 60, 233 (2021). [https://doi.org/10.1007/s00526-021-02100-8] | |
dc.identifier.uri | http://hdl.handle.net/10481/70135 | |
dc.description.abstract | We consider in this paper an area functional defined on submanifolds of fixed degree immersed into a graded manifold equipped with a Riemannian metric. Since the expression of this area depends on the degree, not all variations are admissible. It turns out that the associated variational vector fields must satisfy a system of partial differential equations of first order on the submanifold. Moreover, given a vector field solution of this system, we provide a sufficient condition that guarantees the possibility of deforming the original submanifold by variations preserving its degree. As in the case of singular curves in sub-Riemannian geometry, there are examples of isolated surfaces that cannot be deformed in any direction. When the deformability condition holds we compute the Euler-Lagrange equations. The resulting mean curvature operator can be of third order. | es_ES |
dc.description.sponsorship | Horizon 2020 Project ref. 777822: GHAIA | |
dc.description.sponsorship | MEC-Feder grants MTM2017-84851-C2-1-P and PID2020-118180GB-I00 | |
dc.description.sponsorship | Junta de Andalucía grants A-FQM-441-UGR18 and P20-00164 | |
dc.description.sponsorship | Research Unit MNat SOMM17/6109 and PRIN 2015 “Variational and perturbative aspects of nonlinear differential problems” | |
dc.description.sponsorship | Universidad de Granada/CBUA | |
dc.language.iso | eng | es_ES |
dc.rights | Atribución-NoComercial-SinDerivadas 3.0 España | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ | * |
dc.subject | Sub-Riemannian manifolds | es_ES |
dc.subject | Graded manifolds | es_ES |
dc.subject | Degree of a submanifold | es_ES |
dc.subject | Admissible variations | es_ES |
dc.subject | Isolated submanifolds | es_ES |
dc.title | Variational formulas for submanifolds of fixed degree | es_ES |
dc.type | info:eu-repo/semantics/article | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/EC/H2020/777822: GHAIA | |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es_ES |
dc.type.hasVersion | info:eu-repo/semantics/publishedVersion |
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