[1] Osserman R. Proof of a conjecture of Nirenberg. Comm Pure Appl Math, 1959, 12:229-232 [2] Fujimoto H. On the number of exceptional values of the Gauss map of minimal surfaces. J Math Soc Japan, 1988, 40:235-247 [3] Moser J. On Harnack's theorem for elliptic differential equations. Comm Pure Appl Math, 1961, 14:577-591 [4] Bombieri E, De Giorgi E, Giusti E. Minimal cones and the Bernstein problem. Invent Math, 1969, 7:243-268 [5] Assimos R, Jost J. The geometry of maximum principles and a Bernstein theorem in codimension 2. arXiv:1811.09869, 2019 [6] Jost J, Xin Y L, Yang L. The regularity of harmonic maps into spheres and applications to Bernstein problems. J Differ Geom, 2012, 90:131-176 [7] Jost J, Xin Y L, Yang L. The Gauss image of entire graphs of higher codimension and Bernstein type theorems. Calc Var Partial Differential Equations, 2013, 47:711-737 [8] Bernstein S. Sur les surfaces définies au moyen de leur courbure moyenne ou totale. Ann Ec Norm Sup, 1910, 27:233-256 [9] Chern S S. On the curvature of a piece of hypersurface in Euclidean space. Abh Math Sem Hamburg, 1965, 29:77-91 [10] Hoffman D A, Osserman R, Schoen R. On the Gauss map of complete surfaces of constant mean curvature in $\mathbb{R}^3$ and $\mathbb{R}^4$. Comment Math Helv, 1982, 57:519-531 [11] Jiang X Y, Sun H J, Zhao P B. Rigidity and gap results for the morse index of self-Shrinkers with any codimension. Results Math, 2019, 74:68 [12] Cheng Q M, Hori H, Wei G. Complete Lagrangian self-shrinkers in $\mathbb{R}^4$. arXiv:1802.02396, 2018 [13] Wang L. A Bernstein type theorem for self-similar shrinkers. Geom Dedicata, 2011, 151:297-303 [14] Ding Q, Xin Y L, Yang L. The rigidity theorems of self-shrinkers via Gauss maps. Adv Math, 2016, 303:151-174 [15] Zhou H. A Bernstein type result for graphical self-shrinkers in $\mathbb{R}^4$. Int Math Res Not, 2018, 21:6798-6815 [16] Abresch U, Langer J. The normalized curve shortening flow and homothetic solutions. J Differ Geom, 1986, 23(2):175-196 [17] Basto-Gonçalves J. The Gauss map for Lagrangean and isoclinic surfaces. arxiv:1304.2237, 2013 [18] Li H, Wang X. New characterizations of the Clifford torus as a Lagrangian self-shrinker. J Geom Anal, 2017, 27:1393-1412 [19] Li X X, Li X. On the Lagrangian angle and the Kähler angle of immersed surfaces in the complex plane $\mathbb{C}^2$. Acta Math Sci, 2019, 39B(6):1695-1712 [20] Little J. On singularities of submanifolds of higher dimensional Euclidean spaces. Ann Mat Pura ed Appl, 1969, 83:261-335 [21] Borisenko A A, Nikolaevskil Y A. Grassman manifolds and the Grassmann image of submanifolds. Usp Mat Nauk, 1991, 46(2):41-83 [22] Lichnerowicz A. Applications harmoniques et variétés kähleriennes//Symposia Mathematica. London:Academic Press, 1969:341-402 [23] Course N. f-Harmonic Maps[D]. Warwick:University of Warwick, 2004 [24] Rimoldi M, Veronelli G. Topology of steady and expanding gradient Ricci solitons via f-harmonic maps. Differ Geom Appl, 2013, 31(5):623-638 [25] Hoffman D A, Osserman R. The Gauss map of surfaces in $\mathbb{R}^n$. J Differ Geom, 1983, 18:733-754 [26] Hoffman D A, Osserman R. The Gauss map of surfaces in $\mathbb{R}^3$ and $\mathbb{R}^4$. Proc London Math Soc, 1985, 50(3):27-56 [27] Cheng X, Zhou D. Volume estimates about shrinkers. Proc Amer Math Soc, 2013, 141:687-696 [28] Smoczyk K. Self-shrinkers of the mean curvature flow in arbitrary codimension. Int Math Res Not, 2005, 48:2983-3004 [29] Colding T H, Minicozzi II W P. Generic mean curvature flow I:generic singularities. Ann Math, 2012, 175:755-833 [30] Enomoto K. The Gauss image of flat surfaces in $\mathbb{R}^4$. Kodai Math J, 1986, 9:19-32 |