Related papers: Regularity of infinitesimal CR automorphisms

In this article we study fine regularity properties for mappings of finite distortion. Our main theorems yield strongly localized regularity results in the borderline case in the class of maps of exponentially integrable distortion.…

We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.

CR singularities of real 4-submanifolds in complex 3-space are classified by using local holomorphic coordinate changes to transform the quadratic coefficients of the real analytic defining equation into a normal form. The quadratic…

We study the problem of holomorphic extension of a smooth CR mapping from a real analytic hypersurface to a real algebraic set in complex spaces of different dimensions.

We study automorphism groups and birational automorphism groups of compact complex surfaces. We show that the automorphism group of such surface $X$ is always Jordan, and the birational automorphism group is Jordan unless $X$ is birational…

Let $G$ be a finite group acting on a connected compact surface $\Sigma$, and $M$ be an integer homology 3-sphere. We show that if each element of $G$ is extendable over $M$ with respect to a fixed embedding $\Sigma\rightarrow M$, then $G$…

In the realm of conformal geometry, we give a classification of the Euclidean hypersurfaces that admit a non-trivial conformal infinitesimal variation. In the restricted case of conformal variations, such a classification was obtained by E.…

We determine all complex hyperelliptic curves with many automorphisms and decide which of their jacobians have complex multiplication.

In this article we present a unified way to smooth certain multiple structures called ropes on smooth varieties. We prove that most ropes of arbitrary multiplicity, supported on smooth curves can be smoothed. By a rope being smoothable we…

We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…

We prove smooth and analytic versions of the classical Schwarz reflection principle for transversal CR mappings between two CR manifolds of hypersurface type.

The present work investigates regular, semiregular, and chiral polytopes of any rank $d\geq 3$, whose automorphism groups are 2-groups. There is a large variety of rather small finite regular or alternating semiregular polytopes with…

It is shown that a formal mapping between two real-analytic hypersurfaces in complex space is convergent provided that neither hypersurface contains a nontrivial holomorphic variety. For higher codimensional generic submanifolds,…

We classify compact complex surfaces whose groups of bimeromorphic selfmaps have bounded finite subgroups. We also prove that the stabilizer of a point in the automorphism group of a compact complex surface of zero Kodaira dimension, as…

In characteristic $p>0$ and for $q$ a power of $p$, we compute the number of nonplanar rational curves of arbitrary degrees on a smooth Hermitian surface of degree $q+1$ under the assumption that the curves have a parametrization given by…

In this paper we study endomorphism rings of finite global dimension over not necessarily normal commutative rings. These objects have recently attracted attention as noncommutative (crepant) resolutions, or NC(C)Rs, of singularities. We…

Cartan's uniqueness theorem does not hold in general for CR mappings, but it does hold under certain conditions guaranteeing extendibility of CR functions to a fixed neighborhood. These conditions can be defined naturally for a wide class…

In this paper we introduce the concept of inflexible $CR$ submanifolds. These are $CR$ submanifolds of some complex Euclidean space such that any compactly supported $CR$ deformation is again globally $CR$ embeddable into some complex…

Given $\varepsilon_0>0$, $I\in \mathbb{N}\cup \{0\}$ and $K_0,H_0\geq0$, let $X$ be a complete Riemannian $3$-manifold with injectivity radius $\mbox{Inj}(X)\geq \varepsilon_0$ and with the supremum of absolute sectional curvature at most…

Suppose that $X$ is a smooth, projective threefold over $\mathbb C$ and that $\phi : X \to X$ is an automorphism of positive entropy. We show that one of the following must hold, after replacing $\phi$ by an iterate: i) the canonical class…