m at h . G T ] 2 4 O ct 2 00 7 Curves of Finite Total Curvature

ar X iv : m at h / 06 06 00 7 v 1 [ m at h . G T ] 1 J un 2 00 6 Curves of Finite Total Curvature

We consider the class of curves of finite total curvature, as introduced by Milnor. This is a natural class for variational problems and geometric knot theory, and since it includes both smooth and polygonal curves, its study shows us connections between discrete and differential geometry. To explore these ideas, we consider theorems of Fáry/Milnor, Schur, Chakerian and Wienholtz. Here we intro...

ar X iv : 0 70 7 . 46 02 v 2 [ m at h . A G ] 2 2 O ct 2 00 7 Geometry of the Theta Divisor of a compactified Jacobian

The object of this paper is the theta divisor of the compactified Jacobian of a nodal curve of genus g. We determine its irreducible components and give it a geometric interpretation. A characterization of hyperelliptic irreducible curves in M g is appended as an application.

ar X iv : m at h / 04 10 61 1 v 1 [ m at h . A G ] 2 8 O ct 2 00 4 ON RATIONAL CUSPIDAL PROJECTIVE PLANE CURVES

ar X iv : h ep - l at / 0 01 00 50 v 1 2 7 O ct 2 00 0 Geometry of 4 d Simplicial Quantum Gravity with a U ( 1 ) Gauge Field ∗

The geometry of 4D simplicial quantum gravity with a U(1) gauge field is studied numerically. The phase diagram shows a continuous transition when gravity is coupled with a U(1) gauge field. At the critical point measurements of the curvature distribution of S 4 space shows an inflated geometry with homogeneous and symmetric nature. Also, by choosing a 4-simplex and fixing the scalar curvature ...

Global Behavior of Curves in a Space of Positive Curvature

It is well known that any geodesic in a complete noncompact space of positive curvature goes to infinity. In this paper, we prove that this is true for more general curves and estimate how fast they go to infinity in terms of their curvature and curvature of the space. 0. Introduction. 0.1. All manifolds, submanifolds and curves here are assumed to be of class C°°. A curve parametrized by its a...