Continuous Boundary Values of Holomorphic Functions on Kähler Domains

LetMbe a complex manifold of dimensionnwhich admits a Kähler metric, and letDbe a relatively compact domain onMwhose boundaryBis a C ∞ submanifold ofMof real codimension one. The object of this paper is to use the potential theory associated with the Laplace-Beltrami operator onMto characterize the continuous functions onBwhich have holomorphic extensions toD.

Normal Variations of Invariant Hypersurfaces of Framed Manifolds

A hypersurface of a globally framed f-manifold (briefly, a framed manifold), does not in general possess a framed structure as one may see by considering the 4-sphere S4 in R5 or S5. For, a hypersurface so endowed carries an almost complex structure, or else, it admits a nonsingular differentiable vector field. Since an almost complex manifold may be considered as being globally framed, with no complementary frames, this situation is in marked contrast with the well known fact that a hypersurface (real codimension 1) of an almost complex manifold admits a framed structure, more specifically, an almost contact structure.