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The Group of Large Diffeomorphisms in General Relativity

Domenico Giulini (1997)

Banach Center Publications

We investigate the mapping class groups of diffeomorphisms fixing a frame at a point for general classes of 3-manifolds. These groups form the equivalent to the groups of large gauge transformations in Yang-Mills theories. They are also isomorphic to the fundamental groups of the spaces of 3-metrics modulo diffeomorphisms, which are the analogues in General Relativity to gauge-orbit spaces in gauge theories.

The iterated version of a translative integral formula for sets of positive reach

Rataj, Jan (1997)

Proceedings of the 16th Winter School "Geometry and Physics"

By taking into account the work of J. Rataj and M. Zähle [Geom. Dedicata 57, 259-283 (1995; Zbl 0844.53050)], R. Schneider and W. Weil [Math. Nachr. 129, 67-80 (1986; Zbl 0602.52003)], W. Weil [Math. Z. 205, 531-549 (1990; Zbl 0705.52006)], an integral formula is obtained here by using the technique of rectifiable currents.This is an iterated version of the principal kinematic formula for q sets of positive reach and generalized curvature measures.

The level crossing problem in semi-classical analysis I. The symmetric case

Yves Colin de Verdière (2003)

Annales de l’institut Fourier

We describe a microlocal normal form for a symmetric system of pseudo-differential equations whose principal symbol is a real symmetric matrix with a generic crossing of eigenvalues. We use it in order to give a precise description of the microlocal solutions.

The level crossing problem in semi-classical analysis. II. The Hermitian case

Yves Colin de Verdière (2004)

Annales de l’institut Fourier

This paper is the second part of the paper ``The level crossing problem in semi-classical analysis I. The symmetric case''(Annales de l'Institut Fourier in honor of Frédéric Pham). We consider here the case where the dispersion matrix is complex Hermitian.

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