Related papers: Affine surface area

We classify surjective self-maps (of degree at least two) of affine surfaces according to the log Kodaira dimension.

In this paper we will first introduce the notion of affine structures on a ringed space and then obtain several properties. Affine structures on a ringed space, arising mainly from complex analytical spaces of algebraic schemes over number…

A generalization of the affine-geometric Wirtinger inequality for curves to hypersurfaces is given.

We survey some old and new results about acyclic (affine) complex surfaces, also called homology planes. We ask several questions and leave open directions for future research.

Let $k$ be any field and $k^s$ its separable closure. Let $X$ be an affine variety over $k$ which is isomorphic to affine $n$-space over the field extension $k^s$. Then $X$ is isomorphic to affine $n$ space over $k$.

The surface science of iron oxides is comprehensively reviewed. For the full abstract please see pdf.

An affine surface is said to be an affine Zoll surface if all affine geodesics close smoothly. It is said to be an affine almost Zoll surface if thru any point, every affine geodesic but one closes smoothly (the exceptional geodesic is said…

For a convex body on the Euclidean unit sphere the spherical convex floating body is introduced. The asymptotic behavior of the volume difference of a spherical convex body and its spherical floating body is investigated. This gives rise to…

We prove that the space of affine, transversal at infinity, non-singular real cubic surfaces has 15 connected components. We give a topological criterion to distinguish them and show also how these 15 components are adjacent to each other…

We study the surface area of an ellipsoid in n-dimensional Euclidean space as the function of the lengths of their major semi-axes. We write down an explicit formula as an integral over the unit sphere, use the formula to derive convexity…

We define the ``volume'' contained by pointed $k$-surfaces, first studied by the author in [9], and we show that this volume is always finite. Likewise, we show that the surface area of a pointed $k$-surface is always finite.

We prove that any smooth rational projective surface over the field of complex numbers has an open covering consisting of 3 subsets isomorphic to affine planes.

We obtain universal affine type estimates for the location of the geometric medians of triangle perimeters and for the location of the geometric medians of triangular domains. At the end, some alternative implementations of the triangle…

We construct families of smooth affine surfaces with pairwise non isomorphic A 1-cylinders but whose A 2-cylinders are all isomorphic. These arise as complements of cuspidal hyperplane sections of smooth projective cubic surfaces.

Employing a centro-affine flow on smooth convex bodies, we generate new centro-affine differential invariants. One class of the newly defined invariants is the object of a sharp isoperimetric inequality, while other new inequalities on…

Several classes of *-algebras associated to the action of an affine transformation are considered, and an investigation of the interplay between the different classes of algebras is initiated. Connections are established that relate…

A characterization of valuations on the space of convex Lipschitz functions whose domain is a polytope in $\mathbb{R}^n$ is obtained. It is shown that every upper semicontinuous, equi-affine and dually epi-translation invariant valuation…

We give geometric interpretations of certain affine invariants of convex bodies. The affine invariants are the p-affine surface areas introduced by Lutwak. The geometric interpretations involve generalizations of the Santal\'o-bodies…

We describe all metric spaces that have sufficently many affine functions. As an application we obtain a metric characterization of linear-convex subsets of Banach spaces.

In this paper we consider convex improper affine maps of the 3-dimensional affine space and classify their singularities. The main tool developed is a generating family with properties that closely resembles the area function for non-convex…