GdT Calcul des Variations

Working group on harmonic maps

Europe/Paris
Salle Picard (1R2-129)

Salle Picard (1R2-129)

Description

This will be a short recap of what we did before the summer, and the occasion to decide in what direction we move on.


List of references :

  • Quantitative estimates:
     

Rupflin, Melanie; Sharp quantitative rigidity results for maps from S2 to S2 of general degree.
https://arxiv.org/abs/2305.17045

Topping, Peter M.; A rigidity estimate for maps from $S^2$ to $S^2$ via the harmonic map flow; Bull. Lond. Math. Soc. 55, No. 1, 338-343 (2023)
https://doi.org/10.1112/blms.12731

Topping, Peter M.; Rigidity in the harmonic map heat flow; J. Differ. Geom. 45, No. 3, 593-610 (1997).
https://doi.org/10.4310/jdg/1214459844

  • Qualitative bubbling for Palais-Smale sequences
     

Ding, Weiyue; Tian, Gang; Energy identity for a class of approximate harmonic maps from surfaces; Commun. Anal. Geom. 3, No. 4, 543-554 (1995). 
https://doi.org/10.4310/CAG.1995.v3.n4.a1

Qing, Jie; On singularities of the heat flow for harmonic maps from surfaces into spheres; Commun. Anal. Geom. 3, No. 2, 297-315 (1995). 
https://doi.org/10.4310/CAG.1995.v3.n2.a4

Wang, Changyou; Bubble phenomena of certain Palais-Smale sequences from surfaces to general targets; Houston J. Math. 22, No. 3, 559-590 (1996).

Parker, Thomas H.; Bubble tree convergence for harmonic maps; J. Differ. Geom. 44, No. 3, 595-633 (1996).
https://doi.org/10.4310/jdg/1214459224

Brézis, Haïm; Coron, Jean-Michel; Convergence of solutions of H-systems or how to blow bubbles; Arch. Ration. Mech. Anal. 89, 21-56 (1985). 
https://doi.org/10.1007/BF00281744