The normal Gauss map of a minimal surface in the model space Sol of solvegeometry is a harmonic map with respect to a certain singular Riemannian metric on the extended complex plane.

Let F/K be an abelian extension of number fields with F either CM or totally real and K totally real. If F is CM and the BrumerStark conjecture holds for F/K, we construct a family of G(F/K)–equivariant Hecke characters for F with infinite type equal to a special value of certain G(F/K)–equivariant L–functions. Using results of Greither–Popescu [19] on the Brumer–Stark conjecture we construct l...

This paper gives an overview over several techniques for detection of features, and in particular sharp features, on point-sampled geometry. In addition, a new technique using the Gauss map is shown. Given an unstructured point cloud, this method computes a Gauss map clustering on local neighborhoods in order to discard all points that are unlikely to belong to a sharp feature. A single paramet...

In this paper we define surfaces of revolution of the 1st, 2nd and 3rd kind as space-like or time-like in 3-dimensional Minkowski space. Then by studying their Gauss maps, Laplacian operators and curvatures, we obtain a new classification of surfaces of revolution with pointwise 1-type Gauss map property.

The work of mathematical giants, such as Lobachevsky, Gauss, Riemann, Klein and Poincaré, to name a few, lies at the foundation of the study of the highly structured Riemann surfaces, which allow definition of holomorphic maps, corresponding to analytic maps in the theory of complex analysis. A topological result of Poincaré states that every path-connected Riemann surface can be realised by a ...