To every real analytic Riemannian manifold M there is associated a complex structure on a neighborhood of the zero section in the real tangent bundle of M . This structure can be uniquely specified in several ways, and is referred to as a Grauert tube. We say that a Grauert tube is entire if the complex structure can be extended to the entire tangent bundle. We prove here that the complex manif...

1. S. Bochner and W. Martin, Several complex variables, Princeton Univ. Press, Princeton, N. J., 1948. 2. C. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1-65. 3. G. B. Folland and E. M. Stein, Estimates for the db complex and analysis on the Heisenberg group, Comm. Pure Appl. Math. 27 (1974), 429-522. 4. B. Fuks, Introduction to the...

On a bounded strictly pseudoconvex domain in $\Bbb{C}^n$, $n>1$, the smoothness of Cheng-Yau solution to Fefferman's complex Monge-Ampere equation up boundary is obstructed by local curvature invariant boundary. For domains $\Bbb{C}^2$ which are diffeomorphic ball, we motivate and consider problem determining whether global vanishing this obstruction implies biholomorphic equivalence unit ball....

we prove a strong convergence result for a sequence generated by halpern's type iteration for approximating a common fixed point of a countable family of quasi-lipschitzian mappings in a real hilbert space. consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

Abstract It is known that the starlikeness plays a central role in complex analysis, similarly as convexity functional analysis. However, if we consider biholomorphisms between domains $${\mathbb {C}}^{n},$$ Cn, apa...

One of the most important properties of a geometric flow is whether it preserves the positivity of various notions of curvature. In the case of the Kähler-Ricci flow, the positivity of the curvature operator (Hamilton [7]), the positivity of the biholomorphic sectional curvature (Bando [1], Mok[8]), and the positivity of the scalar curvature (Hamilton [4]) are all preserved. However, whether th...

In this paper we give a partial affirmative answer to a conjecture of Greene-Wu and Yau. We prove that a complete noncompact Kähler surface with positive and bounded sectional curvature and with finite analytic Chern number c 1 (M) 2 is biholomorphic to C 2. The celebrated theorem of Cheeger–Gromoll–Meyer [3], [10] states that a complete noncompact Riemannian manifold with positive sectional cu...

Consider a holomorphic automorphism acting hyperbolically on an invariant compact set. It has been conjectured that the arising stable manifolds are all biholomorphic to Euclidean space. Such a stable manifold is always equivalent to the basin of a uniformly attracting sequence of maps. The equivalence of such a basin to Euclidean space has been shown under various additional assumptions. Recen...

Let X be an irreducible Hermitian symmetric space of noncompact type and rank r. Let p ∈ X and let K be the isotropy group of p in the group of biholomorphic transformations. Let S denote the symmetric algebra in the holomorphic tangent space to X at p. Then S is multiplicity free as a representation of K and the irreducible constituents are parametrized by r-tuples, (m1, . . . ,mr) with m1 ≥ ·...

We develop a classification theory for real-analytic hypersurfaces in C 2 <mml:annotation encoding="applica...