[1] SIMONS J. Minimal varieties in Riemannian manifolds[J]. Annals of Mathematics (Second Series), 1968, 88(1):62-105. DOI:10.2307/1970556. [2] FLEMING W H. On the oriented plateau problem[J]. Rendiconti Del Circolo Matematico Di Palermo, 1962, 11(1):69-90. DOI:10.1007/BF02849427. [3] GIORGI E D. Una estensione del teorema di Bernstein[J]. Ann Scuola Norm Sup Pisa, 1965, 19(3):79-85. [4] ALMGREN F J. Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem[J]. Annals of Mathematics, 1966:277-292. [5] BOMBIERI E, GIORGI E D, GIUSTI E. Minimal cones and the Bernstein problem[J]. Inventiones Mathematicae, 1969, 7(3):243-268. DOI:10.1007/BF01404309. [6] DO CARMO M, PENG C K. Stable complete minimal surfaces in R3 are planes[J]. Bull Amer Math Soc, 1979, 1(6):903-906. DOI:10.1090/S0273-0979-1979-14689-5. [7] FISCHER-COLBRIE D, SCHOEN R. The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature[J]. Communications on Pure and Applied Mathematics, 1980, 33(2):199-211. DOI:10.1002/cpa.3160330206. [8] DO CARMO M, PENG C K, Stable complete minimal hypersurfaces[C]//Proceedings of the 1980 Beijing Symposium on Differential Equations and Differential Geometry. Beijing:Science Press, 1982:1349-1358. [9] ZHU X H, SHEN Y B. On stable complete minimal hypersurfaces in Rn+1[J]. American Journal of Mathematics, 1998, 120(1):103-116. DOI:10.1353/ajm.1998.0005. [10] WANG Q. On minimal submanifolds in an Euclidean space[J]. Math Nachr, 2003, 261/262(1):176-180. DOI:10.1002/mana.200310120. [11] XIA C, WANG Q. Gap theorems for minimal submanifolds of a hyperbolic space[J]. Journal of Mathematical Analysis and Applications, 2016, 436(2):983-989. DOI:10.1016/j.jmaa.2015.12.050. [12] OLIVEIRA H P D, XIA C. Rigidity of complete minimal submanifolds in a hyperbolic space[J]. Manuscripta Mathematica, 2018(88):1-10. [13] CUNHA A W, DE LIMA H F, DOS SANTOS F R. On the first stability eigenvalue of closed submanifolds in the Euclidean and hyperbolic spaces[J]. Differential Geometry and its Applications, 2017, 52:11-19. DOI:10.1016/j.difgeo.2017.03.002. [14] DE BARROS A A, BRASIL JR A C, DE SOURSA JR L A M. A new characterization of submanifolds with parallel mean curvature vector in Sn+p[J]. Kodai Mathematical Journal, 2004, 27(1):45-56. DOI:10.2996/kmj/1085143788. [15] CHENG S Y, YAU S T. Differential equations on Riemannian manifolds and their geometric applications[J]. Communications on Pure and Applied Mathematics, 1975, 28(3):333-354. DOI:10.1002/cpa.3160280303. [16] CHEUNG L F, LEUNG P F. Eigenvalue estimates for submanifolds with bounded mean curvature in the hyperbolic space[J]. Mathematische Zeitschrift, 2001, 236(3):525-530. DOI:10.1007/PL00004840. [17] HOFFMAN D, SPRUCK J. Sobolev and isoperimetric inequalities for Riemannian submanifolds[J]. Communications on Pure and Applied Mathematics, 1974, 27(6):715-727.
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