@misc{10481/74981,
year = {2022},
month = {5},
url = {http://hdl.handle.net/10481/74981},
abstract = {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.},
organization = {MCIN/AEI PID2020-118137GB-I00
CEX2020-001105-M},
organization = {Junta de Andalucia A-FQM-139-UGR18
P18-FR-4049},
organization = {Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP) 2020/03431-6},
publisher = {Springer},
title = {A quasiconformal Hopf soap bubble theorem},
doi = {10.1007/s00526-022-02222-7},
author = {Gálvez López, José Antonio},
}