TY - JOUR 
A1 - Gálvez, José A.
AU - Mira Carrillo, Pablo
AU - Tassi, Marcos P.
T1 - A quasiconformal Hopf soap bubble theorem
Y1 - 2022
SN - 0944-2669
UR - http://hdl.handle.net/10317/12231
AB - 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.
KW - Matemática Aplicada
KW - 12 Matemáticas
LA - eng
PB - SPRINGER
ER -