Generalization of a formula of Wolpert for balanced geodesic graphs on closed hyperbolic surfaces

who endowed the universal Teichmüller space with a different complex Hilbert manifold structure in which the formula for the Weil–Petersson metric not only converges, but defines

with prescribed energy for a class of second order Hamiltonian systems, including the N-body problem... to denote the Euclidean scalar product of any two vectors x, y

Key words : Closed geodesics, Lustemik-Fet theorem, nonsmooth analysis, p-convex

NOTES. had proved the existence of three closed geodesics without selfintersections on an orientable surface of genus 0. The ellipsoid with three pairwise different

We introduce a new class of autoequivalences of derived categories of co- herent sheaves on smooth projective varieties, which generalizes the notion of spherical twists given in

Theorem 1.6 says that the Weil–Petersson volume of any Weil–Petersson geodesic ball in the thick part of moduli space will decay to 0 as g tends to infinity.. It would be

Thus a small angle of intersection requires that at least one of the geodesies is long. The negative curvature, non-abelian case of F\f) is more complex; the lengths of

We define the intersection i(g, p) of the Riemannian metric of negative curvature g with the geodesic current ^ as the total mass of SM for the measure ^p(^).. The following theorem