Complete surfaces of constant anisotropic mean curvature
Metadatos
Mostrar el registro completo del ítemEditorial
Elsevier
Materia
Constant anisotropic mean curvature Wulff shape Classification theorems Multigraph
Fecha
2023-06Referencia bibliográfica
Gálvez López, J.A., Mira, P., Tassi, M. P. Complete surfaces of constant anisotropic mean curvature. Advances in Mathematics 428 (2023) 109137. [https://doi.org/10.1016/j.aim.2023.109137]
Patrocinador
MCIN/AEI /10.13039/501100011033 PID2020-118137GB-I00, CEX2020- 001105-M; CARM; Fundación Séneca-Agencia de Ciencia y Tecnología Región de Murcia 21937/PI/22, 88881.133043/2016-01; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES)Resumen
We study the geometry of complete immersed surfaces in R3 with constant anisotropic mean curvature (CAMC). Assuming that the anisotropic functional is uniformly elliptic, we prove that: (1) planes and CAMC cylinders are the only complete surfaces with CAMC whose Gauss map image is contained in a closed hemisphere of S2; (2) Any complete surface with non-zero CAMC and whose Gaussian curvature does not change sign is either a CAMC cylinder or the Wulff shape, up to a homothety of R3; and (3) if the Wulff shape W of the anisotropic functional is invariant with respect to three linearly independent reflections in R3, then any properly embedded surface of non-zero CAMC, finite topology and at most one end is homothetic to W.