Complete surfaces of constant anisotropic mean curvature Gálvez López, José Antonio Mira, Pablo Tassi, Marcos P. Constant anisotropic mean curvature Wulff shape Classification theorems Multigraph This research has been financially supported by: Projects PID2020-118137GB-I00 and CEX2020- 001105-M, funded by MCIN/AEI /10.13039/501100011033; CARM, Programa Regional de Fomento de la Investigación, Fundación Séneca-Agencia de Ciencia y Tecnología Región de Murcia, reference 21937/PI/22; and Project 88881.133043/2016-01, funded by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES). 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. 2023-07-03T11:13:47Z 2023-07-03T11:13:47Z 2023-06 journal article 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] https://hdl.handle.net/10481/83093 10.1016/j.aim.2023.109137 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Elsevier