ar X iv : 0 71 0 . 20 07 v 2 [ m at h - ph ] 1 9 Fe b 20 08 The wave equation on singular space - times

ar X iv : 0 71 1 . 48 59 v 2 [ m at h . A T ] 1 9 Fe b 20 08 Higher string topology operations

In [2] Chas and Sullivan defined an intersection-type product on the homology of the free loop space LM of an oriented manifoldM. In this paper we show how to extend this construction to a homological conformal field theory of degree d. In particular, we get operations on H∗LM which are parameterized by the twisted homology of the moduli space of Riemann surfaces.

ar X iv : 0 80 2 . 25 80 v 1 [ m at h . G T ] 1 9 Fe b 20 08 3 - Dimensional Schlaefli Formula and Its Generalization

Several identities similar to the Schlaefli formula are established for tetrahedra in a space of constant curvature.

ar X iv : 0 80 2 . 38 70 v 1 [ m at h . A P ] 2 6 Fe b 20 08 GRADIENT NLW ON CURVED BACKGROUND IN 4 + 1 DIMENSIONS

We obtain a sharp local well-posedness result for the Gradient Nonlinear Wave Equation on a nonsmooth curved background. In the process we introduce variable coefficient versions of Bourgain’s X spaces, and use a trilinear multiscale wave packet decomposition in order to prove a key trilinear estimate.

ar X iv : 0 80 2 . 44 39 v 1 [ m at h . D G ] 2 9 Fe b 20 08 Poisson geometry and first integrals of geostrophic equations

We describe first integrals of geostrophic equations, which are similar to the enstrophy invariants of the Euler equation for an ideal incompressible fluid. We explain the geometry behind this similarity, give several equivalent definitions of the Poisson structure on the space of smooth densities on a symplectic manifold, and show how it can be obtained via the Hamiltonian reduction from a sym...

ar X iv : m at h - ph / 0 30 20 21 v 1 1 0 Fe b 20 03 Phase turbulence in the Complex Ginzburg – Landau equation via Kuramoto – Sivashinsky