Related papers: Pseudoholomorphic discs near an elliptic point

This paper presents a few remarks about the topology of symplectic hyperplane sections and the geometry of their complements. In particular, it contains a detailed proof of the following result already stated with hints in [Gi]: for…

We prove:(1) the existence, for every integer n > 3, of a noncompact smooth n-dimensional topological manifold whose diffeomorphism group contains an isomorphic copy of every finitely presented group; (2) a finiteness theorem on finite…

Based on a novel discretization procedure which has recently been proposed and applied in the construction of a canonical discrete analogue of confocal coordinate systems, an explicit method of constructing discrete analogues of ellipsoids…

In this paper we investigate $m$-dimensional complete minimal submanifolds in Euclidean spheres with index of relative nullity at least $m-2$ at any point. These are austere submanifolds in the sense of Harvey and Lawson \cite{harvey} and…

We show that if a compact, connected, and oriented $n$-manifold $M$ without boundary admits a non-constant non-injective uniformly quasiregular self-map, then the dimension of the real singular cohomology ring $H^*(M; \mathbb{R})$ of $M$ is…

We characterize general pseudo-harmonic morphisms from a Riemannian manifold to a Hermitian manifold as pseudo horizontally weakly conformal maps with an additional property. We study to what extent we can (locally) describe these…

We study geometric and topological properties of the image of a smooth submanifold of $\mathbb{R}^{n}$ under a bi-Lipschitz map to $\mathbb{R}^{m}$. In particular, we characterize how the dimension, diameter, volume, and reach of the…

In this paper we study topological surfaces as gridded surfaces in the 2-dimensional scaffolding of cubic honeycombs in Euclidean and hyperbolic spaces.

We study holomorphic symplectic manifolds which are fibred by abelian varieties. This structure is a higher dimensional analogue of an elliptic fibration on a K3 surface. We investigate when a holomorphic symplectic manifold is fibred in…

We prove 3-dimensional hyperbolic cone-manifolds are geometrically inflexible: a cone-deformation of a hyperbolic cone-manifold determines a bi-Lipschitz diffeomorphism between initial and terminal manifolds in the deformation in the…

In this paper we prove the existence of countable branches of rotating patches bifurcating from the ellipses at some implicit angular velocities.

The objective of the paper is to describe Besov spaces on general compact Riemannian manifolds in terms of the best approximation by eigenfunctions of elliptic differential operators.

In this paper, we first prove that the totally real discs lying in certain Levi flat hypersurfaces are polynomially convex. As applications we prove that the totally real discs lying in the boundary of certain polynomial polyhedra are…

Let $\overline{\mathbb{D}}$ be the closure of the unit disk $\mathbb{D}$ in the complex plane $\mathbb{C}$ and $g$ be a continuous function in $\overline{\mathbb{D}}$. In this paper, we discuss some characterizations of elliptic mappings…

We first give an exposition on holomorphic isometries from the Poincar\'e disk to polydisks and from the Poincar\'e disk to the product of the Poincar\'e disk with a complex unit ball. As an application, we provide an example of proper…

We study families of submanifolds in symmetric spaces of compact type arising as exponential images of s-orbits of variable radii. Special attention is given to the cases where the s-orbits are symmetric.

We prove existence of all possible bi-axisymmetric near-horizon geometries of 5-dimensional minimal supergravity. These solutions possess the cross-sectional horizon topology $S^3$, $S^1\times S^2$, or $L(p,q)$ and come with prescribed…

We develop the theory of orbibundles from a geometrical viewpoint using diffeology. One of our goals is to present new tools allowing to calculate invariants of complex hyperbolic disc orbibundles over $2$-orbifolds appearing in the…

In this paper, we proved the existence of Symphonic map from ellipsoid to ellipsoid. We also geive give Hopf construction of Symphonic map from ellipsoid to ellipsoid.

We study the approximation of J-holomorphic maps continuous to the boundary from ma domain in the complex plane into an almost complex manifold by maps J-holomorphic to the boundary, giving partial results in the non-integrable case. For…