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dc.contributor.authorCitti, Giovanna
dc.contributor.authorGiovannardi, Gianmarco
dc.contributor.authorRitoré Cortés, Manuel María 
dc.date.accessioned2021-09-07T09:52:20Z
dc.date.available2021-09-07T09:52:20Z
dc.date.issued2021
dc.identifier.citationCitti, 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.urihttp://hdl.handle.net/10481/70135
dc.description.abstractWe 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.sponsorshipHorizon 2020 Project ref. 777822: GHAIA
dc.description.sponsorshipMEC-Feder grants MTM2017-84851-C2-1-P and PID2020-118180GB-I00
dc.description.sponsorshipJunta de Andalucía grants A-FQM-441-UGR18 and P20-00164
dc.description.sponsorshipResearch Unit MNat SOMM17/6109 and PRIN 2015 “Variational and perturbative aspects of nonlinear differential problems”
dc.description.sponsorshipUniversidad de Granada/CBUA
dc.language.isoenges_ES
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/*
dc.subjectSub-Riemannian manifoldses_ES
dc.subjectGraded manifoldses_ES
dc.subjectDegree of a submanifoldes_ES
dc.subjectAdmissible variationses_ES
dc.subjectIsolated submanifoldses_ES
dc.titleVariational formulas for submanifolds of fixed degreees_ES
dc.typeinfo:eu-repo/semantics/articlees_ES
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/H2020/777822: GHAIA
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses_ES
dc.type.hasVersioninfo:eu-repo/semantics/publishedVersion


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