Mean convex properly embedded [phi, (e)over-right-arrow(3)]-minimal surfaces in R-3 Martínez López, Antonio Martínez Triviño, Antonio Luis phi-minimal surface Mean convex Area estimates Curvature estimates Convexity We establish curvature estimates and a convexity result for mean convex properly embedded [phi, (e) over right arrow (3)]-minimal surfaces in R-3, i.e., phi-minimal surfaces when phi depends only on the third coordinate of R3. Led by the works on curvature estimates for surfaces in 3-manifolds, due to White for minimal surfaces, to Rosenberg, Souam and Toubiana for stable CMC surfaces, and to Spruck and Xiao for stable translating solitons in R-3, we use a compactness argument to provide curvature estimates for a family of mean convex [phi, (e) over right arrow (3)]-minimal surfaces in R-3. We apply this result to generalize the convexity property of Spruck and Xiao for translating solitons. More precisely, we characterize the convexity of a properly embedded [phi, (e) over right arrow (3)]-minimal surface in R-3 with non-positive mean curvature when the growth at infinity of phi is at most quadratic. 2022-07-11T07:27:45Z 2022-07-11T07:27:45Z 2022-05-18 journal article Antonio Martínez, Antonio Luis Martínez-Triviño, João Paulo dos Santos, Mean convex properly embedded [\varphi,\vec{e}_{3}][φ, e 3 ​ ]-minimal surfaces in \mathbb{R}^3R 3 . Rev. Mat. Iberoam. 38 (2022), no. 4, pp. 1349–1370 DOI [10.4171/RMI/1352] http://hdl.handle.net/10481/75919 10.4171/RMI/1352 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional European Mathematical Society