A quasiconformal Hopf soap bubble theorem
Ver/
Compartir
Estadísticas
Ver Estadísticas de usoMetadatos
Mostrar el registro completo del ítemÁrea de conocimiento
Matemática AplicadaPatrocinadores
Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.Realizado en/con
Universidad Politécnica de CartagenaFecha de publicación
2022-05-05Editorial
SPRINGERCita bibliográfica
Gálvez, J.A., Mira, P. & Tassi, M.P. A quasiconformal Hopf soap bubble theorem. Calc. Var. 61, 129 (2022). https://doi.org/10.1007/s00526-022-02222-7Revisión por pares
SIResumen
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.
Colecciones
- Artículos [1734]
El ítem tiene asociados los siguientes ficheros de licencia:
Redes sociales