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© Walter de GruyterWe show that a disc functional on a complex manifold has a plurisubharmonic envelope if all its pullbacks byholomorph ic submersions from domains of holomorphyin affine space do and it is locallybounded above and upper semicontinuous in a certain weak sense. For naturallydefined classes of disc functionals on manifolds, this result reduces a propertysomewhat stronger than having a plurisubharmonic envelope to the affine case. The proof uses a recent Stein neighbourhood construction of Rosay, who proved the plurisubharmonicityof the Poisson envelope on all manifolds. As a consequence, the Riesz envelope and the Lelong envelope are plurisubharmonic on all manifolds; for the former, we make use of new work of Edigarian. The basic theoryof the three main classes of disc functionals is therebyextended to all manifolds.Finnur Lárusson and Ragnar Sigurdsso

Plurisubharmonicity of envelopes of disc functionals on manifolds