A quasiconformal Hopf soap bubble theorem
StatisticsView Usage Statistics
MetadataShow full item record
Knowledge AreaMatemática Aplicada
SponsorsOpen Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.
Realizado en/conUniversidad Politécnica de Cartagena
Bibliographic CitationGálvez, 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
We show that any compact surface of genus zero in R3 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 elliptic Weingarten 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.
- Artículos 
The following license files are associated with this item: