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Given a collection {Z1, Z2,. .. , Zm} of n-sided polygons in the plane and a query polygon W we give algorithms to find all Z ℓ such that W = f (Z ℓ) with f an unknown similarity transformation in time independent of the size of the collection. If f is a known affine transformation, we show how to find all Z ℓ such that W = f (Z ℓ) in O(n + log(m)) time.… (More)

Given real numbers 4π > θ 0 ≥ θ 1 ≥ θ 2 ≥ θ 3 > 0 so that 3 j=0 θ j = 4π, we provide a detailed description of the space of flat met-rics on the 2-sphere with 4 conical points of cone angles θ 0 , θ 1 , θ 2 , θ 3 , endowed with a geometric structure arising from the area function.

- R G Campos, J L López-López, R Vera
- 2006

We present a matrix technique to obtain the spectrum and the analytical index of some elliptic operators defined on compact Riemannian manifolds. The method uses matrix representations of the derivative which yield exact values for the derivative of a trigono-metric polynomial. These matrices can be used to find the exact spectrum of an elliptic operator in… (More)

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