A quasiconformal Hopf soap bubble theorem Gálvez López, José Antonio This research has been financially supported by: Projects PID2020-118137GB-I00 and CEX2020-001105-M, funded by MCIN/AEI/10.13039/501100011033; Junta de Andalucia Grants no. A-FQM-139-UGR18 and P18-FR-4049; and Grant no. 2020/03431-6, Sao Paulo Research Foundation (FAPESP). We showthat any compact surface of genus zero inR3 that satisfies a quasiconformal inequality between its principal curvatures is a round sphere. This solves an old open problem by H. Hopf, and gives a spherical version of Simon’s quasiconformal Bernstein theorem. The result generalizes, among others, Hopf’s theorem for constant mean curvature spheres, the classification of round spheres as the only compact ellipticWeingarten surfaces of genus zero, and the uniqueness theorem for ovaloids by Han, Nadirashvili and Yuan. The proof relies on the Bers-Nirenberg representation of solutions to linear elliptic equations with discontinuous coefficients. 2022-05-25T07:00:09Z 2022-05-25T07:00:09Z 2022-05-05 info:eu-repo/semantics/article Gálvez, J.A., Mira, P. & Tassi, M.P. A quasiconformal Hopf soap bubble theorem. Calc. Var. 61, 129 (2022). [https://doi.org/10.1007/s00526-022-02222-7] http://hdl.handle.net/10481/74981 10.1007/s00526-022-02222-7 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España Springer