$C^0$-coerciveness of Moser's problem and smoothing area preserving homeomorphisms

Details $C^0$-coerciveness of Moser's problem and smoothing area preserving homeomorphisms $C^0$-coerciveness of Moser's problem and smoothing area preserving homeomorphisms

2006-01-09

arxiv.org/abs/math/0601183v5

Mathematics

Dynamical Systems

The previously indicated flaw in the scheme of the proof on the cube has been corrected. Somewhat different scheme is used rel

Scientific paper

In this paper, we establish the $C^0$-coerciveness of Moser's problem of mapping one smooth volume form to another in terms of the weak topology of measures associated to the volume forms. The proof relies on our analysis of Dacorogna-Moser's solution to Moser's problem of mapping one volume form to the other with the same total mass. As an application, we give a proof of smoothing result of area preserving homeomorphisms and its parametric version in two dimension, (or more generally in any dimension in which the smoothing theorem of homeomorphisms is possible, e.g., in dimension 3 but not necessarily in dimension 4). This in turn results in coincidence of the area-preserving homeomorphism group and the symplectic homeomorphism group in two dimension.

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