On analytic mappings among algebroid surfaces

Analytic Mappings on Hyperfinite Sets

Let S and T be hyperfinite sets in an N]-saturated nonstandard universe. The following are equivalent: m 1*1 ~ l (l) rff ~ • • (ii) There is a bijection from 5 onto T whose graph is Borel (over the internal subsets of S x T). This follows from somewhat more general results about analytic partial functions on hyperfinite sets, the proofs of which use Choquet's theorem on the capacitibility of an...

Mappings On Decomposable Combinatorial Structures: Analytic Approach

Combinatorics, Probability & Computing / Volume 11 / Issue 01 / January 2002, pp 61 78 DOI: 10.1017/S0963548301005016, Published online: 14 February 2002 Link to this article: http://journals.cambridge.org/abstract_S0963548301005016 How to cite this article: E. MANSTAVICIUS (2002). Mappings on Decomposable Combinatorial Structures: Analytic Approach. Combinatorics, Probability & Computing, 11, ...

Complex Analytic Mappings

Morse theory for analytic functions on surfaces

In this paper we deal with analytic functions f : S → R defined on a compact two dimensional Riemannian surface S whose critical points are semi degenerated (critical points having a non identically vanishing Hessian). To any element p of the set of semi degenerated critical points Q we assign an unique index which can take the values −1, 0 or 1, and prove that Q is made up of finitely many (cr...

Quasihomogeneous analytic affine connections on surfaces

We classify torsion-free real-analytic affine connections on compact oriented real-analytic surfaces which are locally homogeneous on a nontrivial open set, without being locally homogeneous on all of the surface. In particular, we prove that such connections exist. This classification relies in a local result that classifies germs of torsion-free real-analytic affine connections on a neighborh...