Variational formulas for submanifolds of fixed degree Citti, Giovanna Giovannardi, Gianmarco Ritoré Cortés, Manuel María Sub-Riemannian manifolds Graded manifolds Degree of a submanifold Admissible variations Isolated submanifolds 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. 2021-09-07T09:52:20Z 2021-09-07T09:52:20Z 2021 journal article 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] http://hdl.handle.net/10481/70135 eng info:eu-repo/grantAgreement/EC/H2020/777822: GHAIA http://creativecommons.org/licenses/by-nc-nd/3.0/es/ open access Atribución-NoComercial-SinDerivadas 3.0 España