Rectifiability of defect measures, fundamental groups and density of Sobolev mappings

Fang Hua Lin

Journées équations aux dérivées partielles (1996)

  • Volume: 1996, page 1-14
  • ISSN: 0752-0360

How to cite

top

Lin, Fang Hua. "Rectifiability of defect measures, fundamental groups and density of Sobolev mappings." Journées équations aux dérivées partielles 1996 (1996): 1-14. <http://eudml.org/doc/93319>.

@article{Lin1996,
author = {Lin, Fang Hua},
journal = {Journées équations aux dérivées partielles},
keywords = {-harmonic map; Hausdorff dimension; Radon measure},
language = {eng},
pages = {1-14},
publisher = {Ecole polytechnique},
title = {Rectifiability of defect measures, fundamental groups and density of Sobolev mappings},
url = {http://eudml.org/doc/93319},
volume = {1996},
year = {1996},
}

TY - JOUR
AU - Lin, Fang Hua
TI - Rectifiability of defect measures, fundamental groups and density of Sobolev mappings
JO - Journées équations aux dérivées partielles
PY - 1996
PB - Ecole polytechnique
VL - 1996
SP - 1
EP - 14
LA - eng
KW - -harmonic map; Hausdorff dimension; Radon measure
UR - http://eudml.org/doc/93319
ER -

References

top
  1. [AL] F. Almgren, and E. Lieb, Singularities of energy minimizing maps from the ball to the sphere : examples, counterexamples, and bounds. Annals of Math. (2) 128, 1988, no. 3, 483-530. Zbl0673.58013MR91a:58049
  2. [B] F. Bethuel, The approximation problem for Sobolev maps between two manifolds, Acta Math. 167, 1991, 153-206. Zbl0756.46017MR92f:58023
  3. [B2] F. Bethuel, A Characterization of maps in H1 (B3, S2) which can be approximated by smooth maps, Ann. Inst. H. Poincaré, Anal. Nonlineaire 7, 1990, 4, 269-286. Zbl0708.58004MR91f:58013
  4. [BCDH] F. Bethuel, J. M. Coron, F. Demengel, and F. Helein, A cohomological criterion for density of smooth maps in Sobolev spaces between two manifolds, Nematics Zbl0735.46017
  5. F. Bethuel, J. M. Coron, F. Demengel, and F. Helein, ed. by J. M. Coron et al., NATO ASI Series, Kluwer Academic Publishers, 1990. 
  6. [Bu] F. Burstal, Harmonic maps of finite energy from noncompact manifolds, J. London Math. Soc. 30, 1984, 361-370. Zbl0622.58008MR86c:58033
  7. [BBC] F. Bethuel, H. Brezis, and J. M. Coron, Relaxed energies for harmonic maps, Variational Methods, 1988, 37-52, Birkhauser, Boston, MA, 1990. Zbl0793.58011
  8. [CG] J. M. Coron, and R. Gulliver, Minimizing p-harmonic maps into spheres, J. Reine Angrew Math. 401, 1989, 82-100. Zbl0677.58021MR90m:58040
  9. [GMS] M. Giaquinta, L. Modica, and J. Souček, The Dirichlet energy of mappings with values into the sphere, Manuscripta Math. 65, 1989, 4, 489-507. Zbl0678.49006MR90i:49053
  10. [GMS2] M. Giaquinta, The gap phenomenon for variational integrals in Sobolev spaces, preprint 1991. Zbl0749.58019
  11. [HL] R. Hardt, and F. H. Lin, Mapping minimizing the Lp-norm of the gradient, Comm. Pure and Appl. Math. 40, 1987, 555-588. Zbl0646.49007MR88k:58026
  12. [HL2] R. Hardt, and F. H. Lin, A remark on H1-mappings, Manuscripta Math. 56, 1986, no. 1, 1-10. Zbl0618.58015MR87k:58068
  13. [HLP] R. Hardt, F. H. Lin, and C. C. Poon, Axially symmetric harmonic maps minimizing a relaxed energy, Comm. Pure and Appl. Math. 45, 1992, 417-459. Zbl0769.58012MR93c:58054
  14. [L] F. H. Lin, Rectifiability of defect measures, fundamental groups and density of Sobolev maps, preprint. Zbl0871.35028
  15. [P] D. Preiss, Geometry of measures in ℝn : distribution, rectifiability, and densities, Ann. of Math. (2) 125, 1987, 537-643. Zbl0627.28008MR88d:28008
  16. [SU] R. Schoen, and K. Uhlenbeck, A regularity theory for harmonic maps. J. Diff. Geom. 17, 1982, 307-335. Zbl0521.58021MR84b:58037a
  17. [SU2] R. Schoen, and K. Uhlenbeck, Approximation theorems for Sobolev mappings, preprint, 1984. 
  18. [SY] R. Schoen, and S. T. Yau, The existence of incompressible minimal surfaces and topology of three-dimensional manifolds with non-negative scalar curvature, Ann. of Math. 110, 1979, 127-142. Zbl0431.53051MR81k:58029
  19. [W] B. White, Homotopy classes in Sobolev spaces and existence of energy mminimizing maps, Acta Math. 160, 1988, 1-17. Zbl0647.58016MR89a:58031

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.