Mean convex properly embedded -minimal surfaces in
Antonio MartínezUniversidad de Granada, Spain
Antonio Luis Martínez-TriviñoUniversidad de Granada, Spain
João Paulo dos SantosUniversidade de Brasília, Brasília-Df, Brazil
We establish curvature estimates and a convexity result for mean convex properly embedded -minimal surfaces in , i.e., -minimal surfaces when depends only on the third coordinate of . 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 , we use a compactness argument to provide curvature estimates for a family of mean convex -minimal surfaces in . 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 -minimal surface in with non-positive mean curvature when the growth at infinity of is at most quadratic.
Cite this article
Antonio Martínez, Antonio Luis Martínez-Triviño, João Paulo dos Santos, Mean convex properly embedded -minimal surfaces in . Rev. Mat. Iberoam. 38 (2022), no. 4, pp. 1349–1370DOI 10.4171/RMI/1352