Euler-LagrangeCharacterizationofArea-MinimizingGraphsinRandersSpaceswithNon-constantPotential
Keywords:
Euler-Lagrangeequations,meancurvature1-form,Finslerstructure,Randersmetric,hypersurfaces,minimalgraphs,minimalsurfacesofrevolution.Abstract
WithintheframeworkofRandersspaceswithnon-constantpotential,themeancurvatureformofhy-persurfacesisdetermined,andtheequationswhichcharacterizethearea-minimizinggraphsurfacesareexplicitly derivedasassociatedEuler-LagrangePDEs.Byapplyingtheextendedframeworktotheparticularcaseofgraphs inRandersspaceswithconstantpotential,theknownresultofSouza-Spruck-Tenenblat([27])isconfirmed.Itis shownthattheonlylinearaffinepotentialsforwhichtheRandersmetricadmitsalltheaffineplanesasminimal
graphs,arenecessarilyconstant.Aswell,theODEwhichcharacterizesthegeneratingcurveofsurfacesofrevolu-
tionisderived,thisextendingtheresultobtainedbySouza-Tenenblatin[26]intheconstantpotentialcase.
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