Singular points of harmonic maps from 4-dimensional domains into 3-spheres

Duke Mathematical Journal

Volumn 132, Issue 3, 2006, Pages 531-544

  Nakajima, Tôru ^a  

^a SHIZUOKA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33646518157     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-06-13235-0     Document Type: Article

References (22)

1. F. BETHUEL, On the singular set of stationary harmonic maps, Manuscripta Math. 78 (1993), 417-443. MR 1208652
2. |2] H. BREZIS, J.-M. CORON, and E. H. LIEB, Harmonic maps with defects, Comm. Math. Phys. 107 (1986), 649-705. MR 0868739
3. J.-M. CORON and R. GULLIVER, Minimizing p-harmonic maps into spheres, J. Reine Angew. Math. 401 (1989), 82-100. MR 1018054
4. J. EELLS and L. LEMAIRE, Selected Topics in Harmonic Maps, CBMS Reg. Conf. Ser. Math. 50, Amer. Math. Soc., Providence, 1983. MR 0703510
5. L. C. EVANS, Partial regularity for stationary harmonic maps into spheres, Arch. Rational Mech. Anal. 116(1991), 101 - 113. MR 1143435
6. R. HARDT, "Singularities of harmonic maps" in Nonlinear Partial Differential Equations (Hangzhou, China, 1992), International Academic, Beijing, 1993, 74-80.
7. M.-C. HONG, On the Hausdorff dimension of the singular set of stable-stationary harmonic maps, Comm. Partial Differential Equations 24 (1999), 1967-1985. MR 1720786
8. M.-C. HONG and C.-Y. WANG, On the singular set of stable-stationary harmonic maps, Calc. Var. Partial Differential Equations 9 (1999), 141-156. MR 1714121
9. F.-H. LIN, A remark on the map x/|x|, C. R. Acad. Sci. Paris Sér. I. Math. 305 (1987), 529-531. MR 0916327
10. S. LUCKHAUS, Partial Hölder continuity for minima of certain energies among maps into a Riemannian manifold, Indiana Univ. Math. J. 37 (1988), 349-367. MR 0963506
11. I. MADSEN and J. TORNEHAVE, From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes, Cambridge Univ. Press, Cambridge, 1997. MR 1454127
12. L. MOU, Harmonic maps with prescribed finite singularities, Comm. Partial Differential Equations 14(1989), 1509-1540. MR 1026773
13. H. NAKAJIMA, You's trick (in Japanese), Sūgaku 41 (1989), 253-258. MR 1073362
14. T. NAKAJIMA, Stability and Singularities of Harmonic Maps into Spheres, Tohoku Math. Publ. 26, Tohoku Univ. Math. Inst., Sendai, Japan, 2003. MR 1999770
15. 5 and symmetric spaces, Math. Ann. 298 (1994), 193-205. MR 1256616
16. J. RAMANATHAN, A remark on the energy of harmonic maps between spheres, Rocky Mountain J. Math. 16 (1986), 783-790. MR 0871035
17. R. M. SCHOEN, "Analytic aspects of the harmonic map problem" in Seminar on Nonlinear Partial Differential Equations (Berkeley, Calif., 1983), Math. Sci. Res. Inst. Publ. 2, Springer, New York, 1984, 321 -358. MR 0765241
18. R. SCHOEN and K. UHLENBECK, A regularity theory for harmonic maps, J. Differential Geom. 17 (1982), 307-335. MR 0664498
19. _, Boundary regularity and the Dirichlet problem for harmonic maps, J. Differential Geom. 18 (1983), 253-268. MR 0710054
20. _, Regularity of minimizing harmonic maps into the sphere, Invent. Math. 78 (1984), 89-100. MR 0762354
21. L. SIMON, Theorems on regularity and singularity of energy minimizing maps, Lectures Math. ETH Zürich, Birkhäuser, Basel, 1996. MR 1399562
22. R. T. SMITH, Harmonic mappings of spheres, Amer. J. Math. 97 ( 1975), 364-385. MR 0391127