Filling holes under non-linear constraints Custódio, Ana Luisa Fortes Escalona, Miguel Ángel Sajo-Castelli, A. M. In this paper we handle the problem of filling the hole in the graphic of a surface by means of a patch that joins the original surface with C1-smoothness and fulfills an additional non-linear geometrical constraint regarding its area or its mean curvature at some points. Furthermore, we develop a technique to estimate the optimum area that the filling patch is expected to have that will allow us to determine optimum filling patches by means of a system of linear and quadratic equations. We present several numerical and graphical examples showing the effectiveness of the proposed method. 2023-02-20T07:40:29Z 2023-02-20T07:40:29Z 2023 journal article Custódio, A.L., Fortes, M.A. & Sajo-Castelli, A.M. Filling holes under non-linear constraints. Comp. Appl. Math. 42, 72 (2023). [https://doi.org/10.1007/s40314-023-02210-3] https://hdl.handle.net/10481/80058 10.1007/s40314-023-02210-3 eng open access Springer Nature