Induced trajectories and approximate inertial manifolds
Infinite geodesic rays in the space of Kähler potentials
In this paper we prove the existence of solutions of a degenerate complex Monge-Ampére equation on a complex manifold. Applying our existence result to a special degeneration of complex structure, we show how to associate to a change of complex structure an infinite length geodetic ray in the space of potentials. We also prove an existence result for the initial value problem for geodesics. We end this paper with a discussion of a list of open problems indicating how to relate our reults to the...
Infinitesimal conjugacies and Weil-Petersson metric
We study deformations of compact Riemannian manifolds of negative curvature. We give an equation for the infinitesimal conjugacy between geodesic flows. This in turn allows us to compute derivatives of intersection of metrics. As a consequence we obtain a proof of a theorem of Wolpert.
Infinitesimal differential geometry.
Instanton moduli as a novel map from tori to K3-surfaces.
Integration and the Feynman-Kac formula
Intertwined mappings
Invariants analytiques des champs de vecteurs de
On démontre qu’il ne peut exister de système complet d’invariants analytiques pour l’action du groupe des germes des difféomorphismes sur les champs de vecteurs pour un champ dont la forme normale a un champ réduit associé nul.
Invertible cohomological field theories and Weil-Petersson volumes
We show that the generating function for the higher Weil–Petersson volumes of the moduli spaces of stable curves with marked points can be obtained from Witten’s free energy by a change of variables given by Schur polynomials. Since this generating function has a natural extension to the moduli space of invertible Cohomological Field Theories, this suggests the existence of a “very large phase space”, correlation functions on which include Hodge integrals studied by C. Faber and R. Pandharipande....
Isoliertheit und Stabilität von Flächen konstanter mittlerer Krümmung.
Ito equation as a geodesic flow on
The Ito equation is shown to be a geodesic flow of metric on the semidirect product space , where is the group of orientation preserving Sobolev diffeomorphisms of the circle. We also study a geodesic flow of a metric.