Displaying similar documents to “A minimising property of the radial projection.”

Differential geometry of grassmannians and the Plücker map

Sasha Anan’in, Carlos Grossi (2012)

Open Mathematics

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Using the Plücker map between grassmannians, we study basic aspects of classic grassmannian geometries. For ‘hyperbolic’ grassmannian geometries, we prove some facts (for instance, that the Plücker map is a minimal isometric embedding) that were previously known in the ‘elliptic’ case.

On pairs of closed geodesics on hyperbolic surfaces

Nigel J. E. Pitt (1999)

Annales de l'institut Fourier

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In this article we prove a trace formula for double sums over totally hyperbolic Fuchsian groups Γ . This links the intersection angles and common perpendiculars of pairs of closed geodesics on Γ / H with the inner products of squares of absolute values of eigenfunctions of the hyperbolic laplacian Δ . We then extract quantitative results about the intersection angles and common perpendiculars of these geodesics both on average and individually.

Large dimensional sets not containing a given angle

Viktor Harangi (2011)

Open Mathematics

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We say that a set in a Euclidean space does not contain an angle α if the angle determined by any three points of the set is not equal to α. The goal of this paper is to construct compact sets of large Hausdorff dimension that do not contain a given angle α ∈ (0,π). We will construct such sets in ℝn of Hausdorff dimension c(α)n with a positive c(α) depending only on α provided that α is different from π/3, π/2 and 2π/3. This improves on an earlier construction (due to several authors)...