ar X iv : 0 90 3 . 32 09 v 1 [ m at h . D G ] 1 8 M ar 2 00 9 Uniform Approximation by Algebraic Minimal Surfaces in R 3

ar X iv : 0 90 1 . 18 06 v 1 [ m at h . A G ] 1 3 Ja n 20 09 GREENBERG APPROXIMATION AND THE GEOMETRY OF ARC SPACES

We study the differential properties of generalized arc schemes and geometric versions of Kolchin’s Irreducibility Theorem over arbitrary base fields. As an intermediate step, we prove an approximation result for arcs by algebraic curves.

ar X iv : 0 90 2 . 32 39 v 1 [ m at h . D G ] 1 8 Fe b 20 09 Gauge theory in higher dimensions , II

ar X iv : 0 90 4 . 09 09 v 1 [ m at h . FA ] 6 A pr 2 00 9 On Sobolev extension domains in R

We describe a class of Sobolev W k p -extension domains Ω ⊂ R n determined by a certain inner subhyperbolic metric in Ω. This enables us to characterize finitely connected Sobolev W 1 p -extension domains in R 2 for each p > 2 .

ar X iv : 0 80 4 . 34 06 v 1 [ m at h . A P ] 2 1 A pr 2 00 8 REGULARITY OF NON - CHARACTERISTIC MINIMAL GRAPHS IN THE HEISENBERG GROUP

Minimal surfaces in the sub-Riemannian Heisenberg group can be constructed by means of a Riemannian approximation scheme, as limit of Riemannian minimal surfaces. We study the regularity of Lipschitz, non-characteristic minimal surfaces which arise as such limits. Our main results are a-priori estimates on the solutions of the approximating Riemannian PDE and the ensuing C∞ regularity of the su...

ar X iv : 0 90 3 . 01 12 v 1 [ m at h . G T ] 2 8 Fe b 20 09 Coverings and Minimal Triangulations of 3 – Manifolds

This paper uses results on the classification of minimal triangulations of 3-manifolds to produce additional results, using covering spaces. Using previous work on minimal triangulations of lens spaces, it is shown that the lens space L(4k,2k − 1) and the generalised quaternionic space S/Q4k have complexity k, where k ≥ 2. Moreover, it is shown that their minimal triangulations are unique. AMS ...