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A Fatou-Julia decomposition of transversally holomorphic foliations

Taro Asuke (2010)

Annales de l’institut Fourier

A Fatou-Julia decomposition of transversally holomorphic foliations of complex codimension one was given by Ghys, Gomez-Mont and Saludes. In this paper, we propose another decomposition in terms of normal families. Two decompositions have common properties as well as certain differences. It will be shown that the Fatou sets in our sense always contain the Fatou sets in the sense of Ghys, Gomez-Mont and Saludes and the inclusion is strict in some examples. This property is important when discussing...

A fixed point formula of Lefschetz type in Arakelov geometry II: A residue formula

Kai Köhler, Damien Roessler (2002)

Annales de l’institut Fourier

This is the second of a series of papers dealing with an analog in Arakelov geometry of the holomorphic Lefschetz fixed point formula. We use the main result of the first paper to prove a residue formula "à la Bott" for arithmetic characteristic classes living on arithmetic varieties acted upon by a diagonalisable torus; recent results of Bismut- Goette on the equivariant (Ray-Singer) analytic torsion play a key role in the proof.

A fully nonlinear version of the Yamabe problem on manifolds with boundary

Aobing Li, Yan Yan Li (2006)

Journal of the European Mathematical Society

We propose to study a fully nonlinear version of the Yamabe problem on manifolds with boundary. The boundary condition for the conformal metric is the mean curvature. We establish some Liouville type theorems and Harnack type inequalities.

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