Mean convex properly embedded [phi, (e)over-right-arrow(3)]-minimal surfaces in R-3
Metadatos
Afficher la notice complèteEditorial
European Mathematical Society
Materia
phi-minimal surface Mean convex Area estimates Curvature estimates Convexity
Date
2022-05-18Referencia bibliográfica
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]
Patrocinador
Spanish Government MTM2016-80313-P; Junta de Andalucia A-FQM-139-UGR18; "Maria de Maeztu" Excellence Unit IMAG - MCIN/AEI CEX2020-001105-M; Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES) 001Résumé
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.