Complete surfaces of constant anisotropic mean curvature

被引：1

作者：

Galvez, Jose A. ^{[1
]}

Mira, Pablo ^{[2
]}

Tassi, Marcos P. ^{[3
]}

机构：

[1] Univ Granada, Dept Geometria & Topol, Inst Matemat IMAG, Granada, Spain

[2] Univ Politecn Cartagena, Dept Matemat Aplicada & Estadist, Cartagena, Spain

[3] Univ Aquila, Dipartimento Ingn & Sci Informaz & Matemat, Laquila, Italy

来源：

ADVANCES IN MATHEMATICS | 2023年 / 428卷

关键词：

Wulff shape; Classification theorems; Multigraph; VARIATIONAL PROBLEMS; HYPERSURFACES; STABILITY; GEOMETRY; THEOREM;

D O I：

10.1016/j.aim.2023.109137

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.& COPY; 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).

引用

页数：27