Introduction: A good understanding of the geometry of a theta divisor Θ of a principally polarized abelian variety (A,Θ) requires a knowledge of properties of its canonical linear system, the Gauss linear system |OΘ(Θ)|. A striking feature of the theta divisor Θ(C) of the Jacobian of a curve C is that the dual of the branch divisor of the associated Gauss map γΘ on Θ, is not a hypersurface as e...

A variational method to non rigid registration of multi-modal image data is presented. A suitable deformation will be determined via the minimization of a morphological, i.e., contrast invariant, matching functional along with an appropriate regularization energy. The aim is to correlate the morphologies of a template and a reference image under the deformation. Mathematically, the morphology o...

In this paper, we prove effective estimates for the number of exceptional values and the totally ramified value number for the Gauss map of pseudo-algebraic minimal surfaces in Euclidean four-space and give a kind of unicity theorem.

We construct a rigorous renormalisation scheme for analytic vector fields on T. We show that iterating this procedure there is convergence to a limit set with a “Gauss map” dynamics on it. This is valid for diophantine frequency vectors.

For any given projective variety Y , we construct a projective variety X ⊂ P whose general fiber of the Gauss map with reduced scheme structure is isomorphic to Y when the characteristic > 0. Mathematics Subject Classification (2000) 14N05

We study that the n−graphs defining by smooth map f : Ω ⊂ R n → R m , m ≥ 2, in R m+n of the prescribed mean curvature and the Gauss image. We derive the interior curvature estimates sup DR(x)

The main goal of this paper is to reveal the geometric meaning of the maximal number of exceptional values of Gauss maps for several classes of immersed surfaces in space forms, for example, complete minimal surfaces in the Euclidean three-space, weakly complete improper affine spheres in the affine three-space and weakly complete flat surfaces in the hyperbolic three-space. For this purpose, w...

Fractional Hamiltonian Monodromy is a generalization of the notion of Hamiltonian Monodromy, recently introduced by N. N. Nekhoroshev, D. A. Sadovskíı and B. I. Zhilinskíı for energy-momentum maps whose image has a particular type of non-isolated singularities. In this paper, we analyze the notion of Fractional Hamiltonian Monodromy in terms of the Gauss-Manin Monodromy of a Riemann surface con...

Under a map T , a point x recurs at rate given by a sequence {rn} near a point x0 if d(T(x), x0) < rn infinitely often. Let us fix x0, and consider the set of those x’s. In this paper, we study the size of this set for expanding maps and obtain its measure and sharp lower bounds on its dimension involving the entropy of T , the local dimension near x0 and the upper limit of 1 n log 1 rn . We ap...

We study the geometry and topology of immersed surfaces in Euclidean 3-space whose Gauss map satis es a certain two-piece-property, and solve the \shadow problem" formulated by H. Wente.