9 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…
Mapping Cylinders and the Oka Principle
Finnur Larusson
We apply concepts and tools from abstract homotopy theory to complex analysis and geometry, continuing our development of the idea that the Oka Principle is about fibrancy in suita…
Model Structures and the Oka Principle
Finnur Larusson
We embed the category of complex manifolds into the simplicial category of prestacks on the simplicial site of Stein manifolds, a prestack being a contravariant simplicial functor…
The third Cauchy-Fantappie formula of Leray
Cezar Joita, Finnur Larusson
We study the third Cauchy-Fantappie formula, an integral representation formula for holomorphic functions on a domain in affine space, presented by Jean Leray in the third paper of…
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…
Excision for simplicial sheaves on the Stein site and Gromov's Oka principle
Finnur Larusson
A complex manifold satisfies the Oka-Grauert property if the inclusion $\Cal O(S,X) \hookrightarrow \Cal C(S,X)$ is a weak equivalence for every Stein manifold , where the s…