17 citations · 17 across the 3 of their papers we have counts for
5 papers
On the de Rham theorem in the globally subanalytic setting
Annette Huber, Tobias Kaiser, Abhishek Oswal
For globally subanalytic manifolds we define de Rham complexes of globally subanalytic differential forms and of constructible differential forms. Whereas the de Rham theorem does…
The Derivative of a Constructible Function is Constructible
Tobias Kaiser
The notion of constructible functions in the setting of tame real geometry has been introduced by Cluckers and Dan Miller in their work on parametric integration of globally subana…
Semialgebraicity of the convergence domain of an algebraic power series
Tobias Kaiser
Given a power series in finitely many variables that is algebraic over the corresponding polynomial ring over a subfield of the reals, we show that its convergence domain is semial…
The Riemann Mapping Theorem for semianalytic domains and o-minimality
Tobias Kaiser
We consider the Riemann Mapping Theorem in the case of a bounded simply connected and semianalytic domain. We show that the germ at 0 of the Riemann map (i.e. biholomorphic map) fr…
Transition maps at non-resonant hyperbolic singularities are o-minimal
Tobias Kaiser, Jean-Philippe Rolin, Patrick Speissegger
We construct a model complete and o-minimal expansion of the field of real numbers such that, for any planar analytic vector field X and any isolated, non-resonant hyperbolic singu…