Satake compactification and the great Picard theorem

On a Theorem of Picard

We extend Picard's theorem on the existence of elliptic solutions of the second kind of linear homogeneous n th-order scalar ordinary diierential equations with coeecients being elliptic functions (associated with a common period lattice) to linear homogeneous rst-order n n systems. In particular, the qualitative structure of the general solution in terms of elliptic and exponential functions, ...

Cartan–Helgason theorem, Poisson transform, and Furstenberg–Satake compactifications

The connections between the objects mentioned in the title are used to give a short proof of the Cartan–Helgason theorem and a natural construction of the compactifications.

Lucas’s Theorem: a Great Theorem

A Picard type theorem for holomorphic curves∗

Let P be complex projective space of dimension m, π : Cm+1\{0} → P the standard projection and M ⊂ P a closed subset (with respect to the usual topology of a real manifold of dimension 2m). A hypersurface in P is the projection of the set of zeros of a non-constant homogeneous form in m+ 1 variables. Let n be a positive integer. Consider a set of hypersurfaces {Hj} j=1 with the property M ∩ ⋂...

Picard ' S Theorem by Douglas Bridges

This paper deals with the numerical content of Picard's Thsorem. Two classically equivalent versions of this theorem are proved which are distinct from a computational point of view. The proofs are elementary, and constructive in the sense of Bishop. A Brouwerian counterexample is given to the original version of the theorem.