2014/11/30 by Paolo Caldiroli
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Anisotropy #Class (philosophy) #Constant (computer programming) #Curvature #Geometric Analysis and Curvature Flows #Geometry #Infinity #Invariant (physics) #Isoperimetric inequality #Mathematical analysis #Mathematical physics #Mathematics #Mean curvature #Minimal surface #Nonlinear Partial Differential Equations #Physics #Pure mathematics #Type (biology) #math.DG
paper · pdf · doi:10.1007/s00205-015-0881-y
27 pages
arxiv created 2015/05/04 · openalex publication_date 2015/05/12 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Capillarity functionals are parameter invariant functionals defined on classes of two-dimensionals parametric surfaces in R3 as the sum of the area integral with an anisotropic term of suitable form. In the class of parametric surfaces with the topological type of S2 and with fixed volume, extremals of capillarity functionals are surfaces whose mean curvature is prescribed up to a constant. For a certain class of anisotropies vanishing at infinity, we prove existence and nonexistence of volume- constrained, S2-type, minimal surfaces for the corresponding capillarity functionals. Moreover, in some cases, we show existence of extremals for the full isoperimetric inequality.