Compact complex surfaces containing global strongly pseudoconvex hypersurfaces

On the Winding of Pseudoconvex Hypersurfaces along Compact Complex Varieties

SEMI - GLOBAL SOLUTIONS OF ∂̄ b WITH L p ( 1 ≤ p ≤ ∞ ) BOUNDS ON STRONGLY PSEUDOCONVEX REAL HYPERSURFACES

Let M be an open subset of a compact strongly pseudoconvex hypersurface {ρ = 0} defined by M = D × Cn−m ∩ {ρ = 0}, where 1 ≤ m ≤ n− 2, D = {σ(z1, . . . , zm) < 0} ⊂ Cm is strongly pseudoconvex in Cm. For ∂̄b closed (0, q) forms f on M , we prove the semi-global existence theorem for ∂̄b if 1 ≤ q ≤ n−m−2, or if q = n−m− 1 and f satisfies an additional “moment condition”. Most importantly, the solu...

Embedding Compact Strongly Pseudoconvex Cr Manifolds of Class C

In this paper we derive maximal pointwise Hölder estimates for the Kohn’s Laplacian on strongly pseudoconvex CR manifolds of class C3 using the Tanaka-Webster Pseudohermitian metric. The estimates can be used to improve the Boutet De Monvel’s embedding theorem for strongly pseudoconvex compact CR manifolds of real dimension greater or equal to five with less smoothness assumption.

Holomorphic Approximation on Compact Pseudoconvex Complex Manifolds

Let M be a smoothly bounded compact pseudoconvex complex manifold of finite type in the sense of D’Angelo such that the complex structure of M extends smoothly up to bM . Let m be an arbitrary nonnegative integer. Let f be a function in H(M) ∩Hm(M), where Hm(M) is the Sobolev space of order m. Then f can be approximated by holomorphic functions on M in the Sobolev space Hm(M). Also, we get a ho...

A Hodge decomposition theorem on strongly pseudoconvex compact complex Finsler manifolds

In this paper, we prove that the Hodge-Laplace operator on strongly pseudoconvex compact complex Finsler manifolds is a self-adjoint elliptic operator. Then, from the decomposition theorem for self-adjoint elliptic operators, we obtain a Hodge decomposition theorem on strongly pseudoconvex compact complex Finsler manifolds. M.S.C. 2010: 53C56, 32Q99.