@misc{10481/75919,
year = {2022},
month = {5},
url = {http://hdl.handle.net/10481/75919},
abstract = {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.},
organization = {Spanish Government	MTM2016-80313-P},
organization = {Junta de Andalucia	A-FQM-139-UGR18},
organization = {"Maria de Maeztu" Excellence Unit IMAG - MCIN/AEI	CEX2020-001105-M},
organization = {Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES)	001},
publisher = {European Mathematical Society},
keywords = {phi-minimal surface},
keywords = {Mean convex},
keywords = {Area estimates},
keywords = {Curvature estimates},
keywords = {Convexity},
title = {Mean convex properly embedded [phi, (e)over-right-arrow(3)]-minimal surfaces in R-3},
doi = {10.4171/RMI/1352},
author = {Martínez López, Antonio and Martínez Triviño, Antonio Luis},
}