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J -holomorphic discs and real analytic hypersurfaces

William Alexandre, Emmanuel Mazzilli (2014)

Annales de l’institut Fourier

We give in 6 a real analytic almost complex structure J , a real analytic hypersurface M and a vector v in the Levi null set at 0 of M , such that there is no germ of J -holomorphic disc γ included in M with γ ( 0 ) = 0 and γ x ( 0 ) = v , although the Levi form of M has constant rank. Then for any hypersurface M and any complex structure J , we give sufficient conditions under which there exists such a germ of disc.

Jacobi-Eisenstein series of degree two over Cayley numbers.

Minking Eie (2000)

Revista Matemática Iberoamericana

We shall develop the general theory of Jacobi forms of degree two over Cayley numbers and then construct a family of Jacobi- Eisenstein series which forms the orthogonal complement of the vector space of Jacobi cusp forms of degree two over Cayley numbers. The construction is based on a group representation arising from the transformation formula of a set of theta series.

Jensen measures and unbounded B - regular domains in C n

Quang Dieu Nguyen, Dau Hoang Hung (2008)

Annales de l’institut Fourier

Following Sibony, we say that a bounded domain Ω in C n is B -regular if every continuous real valued function on the boundary of Ω can be extended continuously to a plurisubharmonic function on Ω . The aim of this paper is to study an analogue of this concept in the category of unbounded domains in C n . The use of Jensen measures relative to classes of plurisubharmonic functions plays a key role in our work

Jensen measures, hyperconvexity and boundary behaviour of the pluricomplex Green function

Magnus Carlehed, Urban Cegrell, Frank Wikström (1999)

Annales Polonici Mathematici

We characterise hyperconvexity in terms of Jensen measures with barycentre at a boundary point. We also give an explicit formula for the pluricomplex Green function in the Hartogs triangle. Finally, we study the behaviour of the pluricomplex Green function g(z,w) as the pole w tends to a boundary point.

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