Area growth and rigidity of surfaces without conjugate points

Exponential Growth of Spaces without Conjugate Points

An n-dimensional polyhedral space is a length space M (with intrinsic metric) triangulated into n-simplexes with smooth Riemannian metrics. In the definitions below, we assume that the triangulation is fixed. The boundary of M is the union of the (n− 1)-simplexes of the triangulation that are adjacent to only one (n− 1)-simplex. As usual, a geodesic in M is a naturally parametrized locally shor...

Convex Hamiltonians without Conjugate Points

Introduction.

Piecewise monotone maps without periodic points: Rigidity, measures and complexity.

Piecewise monotone maps without periodic points : Rigidity , measures and complexity

We consider piecewise monotone maps of the interval with zero entropy or no periodic points. First, we give a rigid model for these maps: the interval translations mappings, possibly with ips. It follows, e.g., that the complexity of a piecewise monotone map of the interval is at most polynomial if and only if this map has a nite number of periodic points up to monotone equivalence. Second, we ...

Real K 3 Surfaces without Real Points ,

We consider an equivariant analogue of a conjecture of Borcherds. Let (Y,σ) be a real K3 surface without real points. We shall prove that the equivariant determinant of the Laplacian of (Y,σ) with respect to a σ-invariant Ricci-flat Kähler metric is expressed as the norm of the Borcherds Φ-function at the “period point”. Here the period of (Y,σ) is not the one in algebraic geometry.