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A self-contraction of an infinite graph is translating if it stabilizes no non-empty finite set of vertices. To each translating self-contractionf of a graph G is associated a particular end ofG, which is called the direction off. This generalizes the concept of direction of a translation...
We prove that, for an analytic family of “weakly tame” regular functions on an affine manifold, the spectrum at infinity of each function of the family is semicontinuous in the sense of Varchenko.
For anyn ≥ 2, we give examples of almost Kähler conformally flat manifoldsM2n which are not Kähler. We discuss the meaning of these examples in the context of the Goldberg conjecture on almost Kahler manifolds.
Let G be a commutative semigroup and letL be a complete Archimedean Riesz Space. Suppose thatF: G → L satisfies for somee ∈ L+ the...
It is shown that every equi-affine invariant and upper semicontinuous valuation on the space of convex discs is a linear combination of the Euler characteristic, area, and affine length. Asymptotic formulae for approximation of convex discs by polygons are derived, extending results of L. Fejes...
We study surfaces with plane lines of curvature in the framework of Laguerre geometry and provide explicit representation formulae for these surfaces in terms of a potential function. As an application, we explicitly integrate allL- minimal surfaces with plane curvature lines.
In this paper we prove the Magid-Ryan conjecture for 4-dimensional affine hyperspheres in R5. This conjecture states that every affine hypersphere with non-zero Pick invariant and constant sectional curvature is affinely equivalent with either (x12 ±x22)(x32 ±x42...(x2m−12 ±x2m2) = 1 or (x12...
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