Fefferman's Hypersurface Measure and Volume Approximation Problems.

[摘要] In this thesis, we give some alternate characterizations of Fefferman;;s hypersurface measure on the boundary of a strongly pseudoconvex domain in complex Euclidean space. Our results exhibit a common theme: we connect Fefferman;;s measure to the limiting behavior of the volumes of the gap between a domain and its (suitably chosen) approximants. In one approach, these approximants are polyhedral objects with increasing complexity --- a construction inspired by similar results in convex geometry. In our second approach, the super-level sets of the Bergman kernel is the choice of approximants. In both these cases, we provide examples of some (non-strongly) pseudoconvex domains where these alternate characterizations lead to boundary measures that are invariant under volume-preserving biholomorphisms, thus extending the scope of Fefferman;;s original definition.

[发布机构] University of Michigan

[效力级别] s measure

[关键词] Fefferman"s measure;Polyhedral approximations in complex analysis;volume-preserving biholomorphisms;Mathematics;Science;Mathematics