Related papers: Analytic continuation of a biholomorphic mapping

Using recent development in Poletsky theory of discs, we prove the following result: Let $X,$ $Y$ be two complex manifolds, let $Z$ be a complex analytic space which possesses the Hartogs extension property, let $A$ (resp. $B$) be a non…

This article mainly aims to overview the recent efforts on developing algebraic geometry for an arbitrary compact almost complex manifold. We review the results obtained by the guiding philosophy that a statement for smooth maps between…

We give some results concerning the smoothness of the image of a real-analytic submanifold in complex space under the action of a finite holomorphic mapping. For instance, if the submanifold is not contained in a proper complex subvariety,…

In this paper, we solve affirmatively B.-Y. Chen's conjecture for hypersurfaces in the Euclidean space, under a generic condition. More precisely, every biharmonic hypersurface of the Euclidean space must be minimal if their principal…

We consider a smooth CR mapping $f$ from a real-analytic generic submanifold $M$ in $\bC^N$ into $\bC^N$. For $M$ of finite type and essentially finite at a point $p\in M$, and $f$ formally finite at $p$, we give a necessary and sufficient…

We prove that every smooth rigid spherical hypersurface in ${\mathbb C}^2$ is in fact real-analytic. As an application of this result, it follows that the classification of real-analytic rigid spherical hypersurfaces in ${\mathbb C}^2$…

We show that biholomorphic mappings between two bounded, pseudoconvex domains with smooth boundary extend smoothly to the boundaries of the domains, under a regularity condition on a family of twisted Bergman-like projections. This result…

We prove that a real-valued function (that is not assumed to be continuous) on a real analytic manifold is analytic whenever all its restrictions to analytic submanifolds homeomorphic to the 2-sphere are analytic. This is a real analog for…

Gangbo and McCann showed that optimal transportation between hypersurfaces generally leads to multivalued optimal maps - bivalent when the target surface is strictly convex. In this paper we quantify H\"older continuity of the bivalent map…

First, we classify proper biharmonic Hopf real hypersurfaces in $\mathbb{C}P^2$. Next, we classify proper biharmonic real hypersurfaces with two distinct principal curvatures in $\mathbb{C}P^n$, where $n\geq 2$. Finally, we prove that…

We study the real analyticity of a CR mapping on the hypersurface $\h$ defined by $\h=\{z\in\C^n,\Re(z_n)+|z'|^2=0\}$ in model almost complex manifolds. We make use of a method of prolongation for the tangential Cauchy-Riemann equations and…

We prove an existence theorem for convex hypersurfaces of prescribed Gauss curvature in the complement of a compact set in Euclidean space which are close to a cone.

The bending map of a hyperbolic 3-manifold maps a convex cocompact hyperbolic metric on a hyperbolic 3-manifold with boundary to its bending measured geodesic lamination. In the present paper we study the extension of this map to the space…

We give a necessary and sufficient condition for the smooth extension of a diffeomorphism between smooth strictly pseudoconvex domains in four real dimensional almost complex manifolds. The proof is mainly based on a reflection principle…

It has been conjectured that every stable manifold arising from a holomorphic automorphism, that acts hyperbolically on a compact invariant set, is biholomorphic to complex Euclidean space. Such stable manifolds are known to be…

We define and study an extended hyperbolic space which contains the hyperbolic space and de Sitter space as subspaces and which is obtained as an analytic continuation of the hyperbolic space. The construction of the extended space gives…

Answering a problem raised by Lazarsfeld, Hwang and Mok proved that a surjective holomorphic map from a rational homogeneous space of Picard number 1 onto projective manifold different from projective space must be a biholomorphism. THe aim…

A topological space $X$ is called $\Cal A$-real compact, if every algebra homomorphism from $\Cal A$ to the reals is an evaluation at some point of $X$, where $\Cal A$ is an algebra of continuous functions. Our main interest lies on…

We show that a compact, complex analytic space $X$ has a bimeromorphic orbifold modification that is an isomorphism over the locally trivial orbifold locus of $X$.

Implementations of known reductions of the Strong Real Jacobian Conjecture (SRJC), to the case of an identity map plus cubic homogeneous or cubic linear terms, and to the case of gradient maps, are shown to preserve significant algebraic…