The Geometry of Convex Affine Maximal Graphs
نویسنده
چکیده
Locally strongly convex surfaces which are extremal for the first variation of the equiaffine area integral have been investigated on several occasions. Here we are interested in the description of their behaviour at infinity. We consider an affine maximal annular end which is a graph of vertical flux and give a detailed representation of it when its affine conormal map works well at infinity.
منابع مشابه
Affine complete locally convex hypersurfaces
An open problem in affine geometry is whether an affine complete locally uniformly convex hypersurface in Euclidean (n + 1)-space is Euclidean complete for n ≥ 2. In this paper we give the affirmative answer. As an application, it follows that an affine complete, affine maximal surface in R3 must be an elliptic paraboloid.
متن کاملTriple factorization of non-abelian groups by two maximal subgroups
The triple factorization of a group $G$ has been studied recently showing that $G=ABA$ for some proper subgroups $A$ and $B$ of $G$, the definition of rank-two geometry and rank-two coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. In this paper we study two infinite classes of non-abelian finite groups $D_{2n}$ and $PSL(2,2^{n})$...
متن کاملOn the quadratic support of strongly convex functions
In this paper, we first introduce the notion of $c$-affine functions for $c> 0$. Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown.
متن کاملC*-Extreme Points and C*-Faces oF the Epigraph iF C*-Affine Maps in *-Rings
Abstract. In this paper, we define the notion of C*-affine maps in the unital *-rings and we investigate the C*-extreme points of the graph and epigraph of such maps. We show that for a C*-convex map f on a unital *-ring R satisfying the positive square root axiom with an additional condition, the graph of f is a C*-face of the epigraph of f. Moreover, we prove som...
متن کاملVisibility Graphs of Staircase Polygons and the Weak Bruhat Order, I: from Visibility Graphs to Maximal Chains
The recognition problem for visibility graphs of simple polygons is not known to be in NP, nor is it known to be NP-hard. It is, however, known to be in PSPACE. Further, every such visibility graph can be dismantled as a sequence of visibility graphs of convex fans. Any nondegenerate configuration of n points can be associated with a maximal chain in the weak Bruhat order of the symmetric group...
متن کامل