Displaying similar documents to “Asymptotic values of minimal graphs in a disc”

Minimal Graphs in ℍ n × ℝ and ℝ n + 1

Ricardo Sà Earp, Eric Toubiana (2010)

Annales de l’institut Fourier

Similarity:

We construct geometric barriers for minimal graphs in ℍ n × ℝ . We prove the existence and uniqueness of a solution of the vertical minimal equation in the interior of a convex polyhedron in ℍ n extending continuously to the interior of each face, taking infinite boundary data on one face and zero boundary value data on the other faces. In ℍ n × ℝ , we solve the Dirichlet problem for the vertical minimal equation in a C 0 convex domain Ω ⊂ ℍ n taking arbitrarily continuous...

The local regularity of soap films after Jean Taylor

Guy David (2008)

Journées Équations aux dérivées partielles

Similarity:

The following text is a minor modification of the transparencies that were used in the conference; please excuse the often telegraphic style. The main goal of the series of lectures is a presentation (with some proofs) of Jean Taylor’s celebrated theorem on the regularity of almost minimal sets of dimension 2 in ℝ 3 , and a few more recent extensions or perspectives. Some of the results presented below are work of, or with T. De Pauw, V. Feuvrier A. Lemenant, and T. Toro. ...

Combinatorial and group-theoretic compactifications of buildings

Pierre-Emmanuel Caprace, Jean Lécureux (2011)

Annales de l’institut Fourier

Similarity:

Let X be a building of arbitrary type. A compactification 𝒞 sph ( X ) of the set Res sph ( X ) of spherical residues of X is introduced. We prove that it coincides with the horofunction compactification of Res sph ( X ) endowed with a natural combinatorial distance which we call the . Points of 𝒞 sph ( X ) admit amenable stabilisers in Aut ( X ) and conversely, any amenable subgroup virtually fixes a point in 𝒞 sph ( X ) . In addition, it is shown that, provided Aut ( X ) is transitive enough, this compactification also coincides with the group-theoretic...

Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to β -shifts

Veronica Baker, Marcy Barge, Jaroslaw Kwapisz (2006)

Annales de l’institut Fourier

Similarity:

This article is devoted to the study of the translation flow on self-similar tilings associated with a substitution of Pisot type. We construct a geometric representation and give necessary and sufficient conditions for the flow to have pure discrete spectrum. As an application we demonstrate that, for certain beta-shifts, the natural extension is naturally isomorphic to a toral automorphism.