Connecting topological Hopf singularities

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Volumn 2, Issue 2, 2003, Pages 287-344

  Hardt, Robert ^a   Rivière, Tristan ^b  

^a RICE UNIVERSITY   (United States)

^b ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 28444439728     PISSN: 0391173X     EISSN: 20362145     Source Type: Journal    
DOI: None     Document Type: Article

References (36)

1. L. Ambrosio - B. Kirchheim, Currents in metric spaces, Acta Math. 185 (2000), 1-80.
2. F. Bethuel, The approximation problem for Sobolev maps between two manifolds, Acta Math. 167 (1991), 153-206.
3. 2) which can be approximated by smooth maps, Ann. Inst. H. Poincaré Anal. Nonlinaire 7 (1990), 269-286.
4. F. Bethuel, Approximations in trace spaces defined between manifolds, Nonlinear Anal. 24 (1995), 121-130.
5. F. Bethuel - H. Brezis - J.-M. Coron, Relaxed energies for harmonic maps, In: “Variational methods”, 3-52, Progr. Nonlin. Diff. Eqns. Appl. 4, Birkhäuser Boston, 1990.
6. H. Brezis - J.-M. Coron, - E. Lieb, Harmonic maps with defects, Comm. Math. Phys. 107, no. 4 (1986), 649-705.
7. H. Brezis - Y.Y. Li, Topology and Sobolev spaces, preprint, 2000.
8. F. Bethuel - X.M. Zheng, Density of smooth functions between two manifolds in Sobolev spaces, J. Funct. Anal. 80, no. 1 (1988), 60-75.
9. H. Federer, “Geometric measure theory”, Springer-Verlag, Berlin and New York, 1969.
10. Fleming, flat chains over a coefficient group, Trans. Amer. Math. Soc. 121 (1966), 160-186.
11. M. Giaquinta, “Multiple integrals in the calculus of variations and elliptic systems”, Princeton University Press, Princeton, 1983.
12. M. Giaquinta - G. Modica - J. Souček, The Dirichlet energy of mappings with values into the sphere, Manuscripta Math. 65, no. 4 (1989), 489-507.
13. M. Giaquinta - G. Modica - J. Souček, “Cartesian currents in the calculus of variations”. I, II, Springer-Verlag, Berlin, 1998.
14. M. Gromov, “Metric structures for Riemannian and non-Riemannian spaces”, Progress in mathematics 152, Birkhaüser, Boston, 1999.
15. R. Hardt, Uniqueness of nonparametric area minimizing currents, Indiana Univ. Math. J. 26 (1977), 65-71.
16. R. Hardt - T. DePauw, Size minimization and approximating problems, to appear in Calc. Var. Partial Differential Equations.
17. F. Hélein, “Harmonic maps, conservation laws, and moving frames”, Diderot Press, Paris, 1997.
18. F. Hang - Lin, Topology of Sobolev mappings, Math. Res. Lett. 8 (2001), 321-330.
19. F. Hang - F. Lin, Topology of Sobolev mappings II, preprint, 2001.
20. 1 mappings, Manuscripta Math. 56 (1986), 1-10.
21. p norm of the gradient, Comm. Pure. Appl. Math. 15 (1987), 555-588.
22. R. Hardt - T. Rivière, Ensembles singuliers topologiques dans les espaces fonc-tionnels entre variétés, Exp. VII, Sémin. Équ. Dériv. Part., École Polytech., Palaiseau, 2001.
23. 3), in preparation.
24. R. Hardt - T. Rivière, Connecting singularities of arbitrary rational homotopy type, in preparation.
25. 2) (16/5 ≤ p < 4), J. Math. Anal. Appl. 190 (1995), 361-372.
26. T. Isobe, Some new properties of Sobolev mappings: intersection theoretical approach, Proc. Roy. Soc. Edinburgh Sect. A 127 (1997), 337-358.
27. D. Mucci, A characterization of graphs which can be approximated in area by smooth graphs, To appear in the J. Eur. Math. Soc.
28. M. R. Pakzad - T. Rivière, Weak density of smooth maps for the Dirichlet energy between manifolds, preprint, 2000.
29. 2, Comm. Anal. Geom. 6 (1998), 427-483.
30. 1), Ann. Global Anal. Geom. 18 (2000), 517-528.
31. L. Simon, “Lectures on geometric measure theory”, Proc. Centre for Math. Anal. 3, Australian National University, Canberra, 1983.
32. R. Schoen - K. Uhlenbeck, Boundary regularity and the Dirichlet problem for harmonic maps, J. Differential Geom. 18 (1983), 253-268.
33. B. White, Infima of energy functionals in homotopy classes of mappings, J. Differential Geom. 23 (1986), 127-142.
34. B. White, Homotopy classes in Sobolev spaces and the existence of energy minimizing maps, Acta Math. 160 (1988), 1-17.
35. B. White, Rectifiability of flat chains, Ann. Math. (2) 150 (1999), 165-184.
36. Y. Zhou, “On the density of smooth maps in Sobolev spaces between two manifolds”, Ph. D. thesis, Columbia University, 1993.