Gauss maps of the mean curvature flow

Mathematical Research Letters

Volumn 10, Issue 2-3, 2003, Pages 287-299

  Wang, Mu Tao ^a  

^a Columbia University ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042916071     PISSN: 10732780     EISSN: None     Source Type: Journal    
DOI: 10.4310/mrl.2003.v10.n3.a2     Document Type: Article

References (22)

1. R. L. Bishop, B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1-49.
2. J. Cheeger, D. G. Ebin, Comparison theorems in Riemannian geometry, North-Holland Mathematical Library, Vol. 9. North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1975.
3. J. Chen, G. Tian, Moving symplectic curves in Kähler-Einstein surfaces, Acta Math. Sin. (Engl. Ser.) 16 (2000), 541-548.
4. K. Ecker, G. Huisken, Mean curvature evolution of entire graphs, Ann. of Math. (2) 130 (1989), 453-471.
5. _, Interior estimates for hypersurfaces moving by mean curvature, Invent. Math. 105 (1991), 547-569.
6. J. Eells, L. Lemaire, Selected topics in harmonic maps, CBMS Regional Conference Series in Mathematics, 50. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1983.
7. D. Fischer-Colbrie, Some rigidity theorems for minimal submanifolds of the sphere, Acta Math. 145 (1980), 29-46.
8. R. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), 255-306
9. _, Four-manifolds with positive curvature operator, J. Differential Geom. 24 (1986), 153-179.
10. S. Hildebrandt, J. Jost, K.-O. Widman, Harmonic mappings and minimal submanifolds, Invent. Math. 62 (1980/81), 269-298.
11. J. Jost, Y. L. Xin, Bernstein type theorems for higher codimension, Calc. Var. Partial Differential Equations 9 (1999), 277-296.
12. _, A Bernstein theorem for special Lagrangian graphs, Calc. Var. Partial Differential Equations 15 (2002), 299-312.
13. E.A. Ruh, J. Vilms, The tension field of the Gauss map, Trans. Amer. Math. Soc. 149 (1970), 569-573.
14. K. Smoczyk, A canonical way to deform a Lagrangian submanifold, preprint: dg-ga/9605006
15. M.-P. Tsui, M.-T. Wang, A Bernstein type result for special Lagrangian submanifolds, Math. Res. Lett. 9 (2002), 529-535.
16. _, Mean curvature flows and homotopy of maps between spheres, preprint, 2003.
17. M.-T. Wang, Mean curvature flow of surfaces in Einstein four-manifolds, J. Differential Geom. 57 (2001), 301-338.
18. _, Deforming area preserving diffeomorphism of surfaces by mean curvature flow, Math. Res. Lett. 8 (2001), 651-661.
19. _, Long-time existence and convergence of graphic mean curvature flow in arbitrary codimension, Invent. Math. 148 (2002), 525-543.
20. _, On graphic Bernstein type results in higher codimension, Trans. Amer. Math. Soc. 355 (2003), 265-271.
21. _, Subsets of Grassmannians preserved by mean curvature flow, preprint, 2002.
22. Y.-C. Wong, Differential geometry of Grassmann manifolds, Proc. Nat. Acad. Sci. U.S.A. 57 (1967), 589-594.