4 papers · 1 filter
The Siciak-Zahariuta extremal function as the envelope of disc functionals
Finnur Larusson, Ragnar Sigurdsson
We establish disc formulas for the Siciak-Zahariuta extremal function of an arbitrary open subset of complex affine space, generalizing Lempert's formula for the convex case. This…
Plurisubharmonicity of envelopes of disc functionals on manifolds
Finnur Larusson, Ragnar Sigurdsson
We show that a disc functional on a complex manifold has a plurisubharmonic envelope if all its pullbacks by holomorphic submersions from domains of holomorphy in affine space do a…
The Jensen envelope is plurisubharmonic on all manifolds
Finnur Larusson, Ragnar Sigurdsson
The Jensen envelope of an upper semicontinuous function on a complex manifold X is defined at as the infimum of over all Jensen measures centred at x.…
Plurisubharmonic extremal functions, Lelong numbers and coherent ideal sheaves
Finnur Larusson, Ragnar Sigurdsson
We introduce a new type of pluricomplex Green function which has a logarithmic pole along a complex subspace A of a complex manifold X. It is the largest negative plurisubharmonic…