A proof of a quantitative rigidity estimate for single bubbles of degree one via harmonic map heat flow, based on:
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);
and using tools from:
Topping, Peter M., Rigidity in the harmonic map heat flow,
J. Differ. Geom. 45, No. 3, 593-610 (1997).
List of references for this working group:
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
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
