Now showing items 1-5 of 5

• #### Criteria for Algebraicity of Analytic Functions ﻿

[OWP-2018-25] (Mathematisches Forschungsinstitut Oberwolfach, 2018-11-12)
We consider functions defined on an open subset of a nonsingular, either real or complex, algebraic set. We give criteria for an analytic function to be a Nash (resp. regular, resp. polynomial) function. Our criteria depend ...
• #### Demailly’s Notion of Algebraic Hyperbolicity: Geometricity, Boundedness, Moduli of Maps ﻿

[OWP-2018-20] (Mathematisches Forschungsinstitut Oberwolfach, 2018-10-08)
Demailly's conjecture, which is a consequence of the Green-Griffiths-Lang conjecture on varieties of general type, states that an algebraically hyperbolic complex projective variety is Kobayashi hyperbolic. Our aim is to ...
• #### Demailly’s Notion of Algebraic Hyperbolicity: Geometricity, Boundedness, Moduli of Maps (Revised Edition) ﻿

[OWP-2018-20.2] (Mathematisches Forschungsinstitut Oberwolfach, 2020-01-23)
Demailly's conjecture, which is a consequence of the Green-Griffths-Lang conjecture on varieties of general type, states that an algebraically hyperbolic complex projective variety is Kobayashi hyperbolic. Our aim is to ...
• #### Global Variants of Hartogs' Theorem ﻿

[OWP-2018-24] (Mathematisches Forschungsinstitut Oberwolfach, 2018-11-06)
Hartogs' theorem asserts that a separately holomorphic function, defined on an open subset of $\mathbb{C}^n$, is holomorphic in all the variables. We prove a global variant of this theorem for functions defined on an open ...
• #### Real Analyticity is Concentrated in Dimension 2 ﻿

[OWP-2018-23] (Mathematisches Forschungsinstitut Oberwolfach, 2018-11-05)
We prove that a real-valued function on a real analytic manifold is analytic whenever all its restrictions to $2$-dimensional analytic submanifolds are analytic functions. We also obtain analogous results in the framework ...