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Bernstein Type Theorems for Minimal Lagrangian Graphs of Quaternion Euclidean Space

Published online by Cambridge University Press:  11 January 2016

Yuxin Dong ,
Yingbo Han  and
Qingchun Ji
Yuxin Dong
Affiliation:
Department of Mathematics, Southeast University, Nanjing, 211189, P. R. China, yingbohan@163.com
Yingbo Han
Affiliation:
Department of Mathematics, Southeast University, Nanjing, 211189, P. R. China, yingbohan@163.com
Qingchun Ji
Affiliation:
Institute of Mathematics, Fudan University, Shanghai, 200433, P. R. China, And Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education, qingchunji@fudan.edu.cn
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Abstract

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In this paper, we prove some Bernstein type results for n-dimensional minimal Lagrangian graphs in quaternion Euclidean space Hn ≅ R4n . In particular, we also get a new Bernstein Theorem for special Lagrangian graphs in Cn .

Keywords

53A1053A0753C38

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 193 , 2009 , pp. 155 - 167
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2009

References

[1] Ecker, K. and Huisken, G., A Bernstein result for minimal graphs of controlled growth, J. Differential Geom., 31 (1990), no. 2, 397–400.Google Scholar
[2] Hildebrant, S., Jost, J. and Widman, K.-O., Harmonic mappings and minimal sub-manifolds, Invent. Math., 62 (1980/81), no. 2, 269–298.Google Scholar
[3] Fischer-Colbrie, D., Some rigidity theorems for minimal submanifolds of the sphere, Acta Math., 145 (1980), no. 1, 29–46.Google Scholar
[4] Harvey, R. and Lawson, H. B., Calibrated geometries, Acta Math., 148 (1982), 47–157.Google Scholar
[5] Jost, J. and Xin, Y. L., Bernstein type theorems for higher codimension, Calc. Var. Partial Differential Equations, 9 (1999), no. 4, 277–296.Google Scholar
[6] Jost, J. and Xin, Y. L., A Bernstein Theorem for Special Lagrangian Graphs, Calc. Var. and Partial Differential Equations, 15 (2002), 299–312.Google Scholar
[7] Lawson, B. and Osserman, R., Non-exsitence, non-uniqueness and irregularity of solutions to minimal surface system, Acta Math., 139 (1970), 1–17.CrossRefGoogle Scholar
[8] Tsui, M.-P. and Wang, M.-T., A Berstein Type Result for Special Lagrangian Submanifolds, Math. Res. Lett., 9 (2002), no. 4, 529–535.Google Scholar
[9] Wang, M.-T., Long-time exsitence and convergence of graghic mean curvature in arbitrary codimension, Invent. Math., 148 (2002), no. 3, 525–543.CrossRefGoogle Scholar
[10] Wang, M.-T., On graphic Berstein type results in higher codimensions, Trans. Amer. Math. Soc., 355 (2003), no. 1, 265–271.Google Scholar
[11] Yuan, Y., A Bernstein problem for special Lagrangian equaton, Invent. Math., 150 (2002) no. 1, 117–125.Google Scholar