We show relation between sign of Gaussian curvature cuspidal edge and geometric invariants through types singularities Gauss map. Moreover, we define characterize positivity/negativity cusps maps by edges, the curvature.

A new technique for computing the differential invariants of a surface from 3D sample points and normals. It is based on a new conformal geometric approach to computing shape invariants directly from the Gauss map. In the current implementation we compute the mean curvature, the Gauss curvature, and the principal curvature axes at 3D points reconstructed by area-based stereo. The differential i...

Let D be a domain in the complex in-plane and let as: D —• R be a regular minimal surface. Let M(K) be the set of points tu 0. The components of M(K) are of three types: isolated points; simple analytic arcs terminating nowhere in D; analytic Jordan curves in D. Components of the third type are r...

In this paper we study one-parameter families of signed transfer operators P± q associated to the Farey map, as well as two-parameter families of operators for the Gauss map, obtained from the Farey map by inducing. We characterise all the analytic eigenfunctions of P± q with eigenvalue λ not embedded in the continuous spectrum, which for λ = 1 are the period functions for Maass forms studied b...

This is an extension and emendation of recent results on the use of Gauss elimination in multivariate polynomial interpolation and, in particular, ideal interpolation. Let Π ⊂ (IF → IF) be the space of all polynomials in d real (IF = IR) or complex (IF = C) variables. Let Q be an n-row map on Π, i.e., a linear map from Π to IF, and consider the task of solving

We study the algebraic Gauss-Manin system and the algebraic Brieskorn module associated to a polynomial mapping with isolated singularities. Since the algebraic GaussManin system does not contain any information on the cohomology of singular fibers, we first construct a non quasi-coherent sheaf which gives the cohomology of every fiber. Then we study the algebraic Brieskorn module, and show tha...

We study the dynamics of a class of interval translation map on three intervals. We show that in this class the typical ITM is of finite type (reduce to an interval exchange transformation) and that the complement contains a Cantor set. We relate our maps to substitution subshifts. Results on Hausdorff dimension of the attractor and on unique ergodicity are obtained.

The helicoidal surface is a generalization of rotation surface in a Minkowski space. We study helicoidal surfaces in a Minkowski 3-space in terms of their Gauss map and provide some examples of new classes of helicoidal surfaces with constant mean curvature in a Minkowski 3-space.

The increasing rate of the Birkhoff sums in infinite iterated function systems with polynomial decay derivative (for example Gauss map) is studied. For different unbounded potential functions, Hausdorff dimensions sets points whos