Related papers: Infinite bubbling in non-K\"ahlerian geometry

The main theorem of this article provides sufficient conditions for a degree $d$ finite cover $M'$ of a hyperbolic 3-manifold $M$ to be a surface-bundle. Let $F$ be an embedded, closed and orientable surface of genus $g$, close to a minimal…

In the minimal surface theory, the Krust theorem asserts that if a minimal surface in the Euclidean 3-space $\mathbb{E}^3$ is the graph of a function over a convex domain, then each surface of its associated family is also a graph. The same…

One of the main purposes of this paper is to prove that on a complete K\"ahler manifold of dimension $m$, if the holomorphic bisectional curvature is bounded from below by -1 and the minimum spectrum $\lambda_1(M) \ge m^2$, then it must…

Given a sequence of properly embedded minimal surfaces in a $3$-manifold with local bounds on area and genus, we prove subsequential convergence, smooth away from a discrete set, to a smooth embedded limit surface, possibly with…

We prove that every complete non-compact manifold of finite volume contains a (possibly non-compact) minimal hypersurface of finite volume. The main tool is the following result of independent interest: if a region $U$ can be swept out by a…

We give an affirmative answer to a conjecture of Ma. Kato, namely that every compact complex surface $S$ in Kodaira's class $VII_0$ with $b_2(S) > 0$ and $b_2(S)$ rational curves, admits a global spherical shell.

We study holomorphic geometric structures on non-K\"ahler compact complex manifolds with trivial canonical line bundle. For Vaisman Calabi-Yau manifolds we prove that all holomorphic geometric structures of affine type on them are locally…

We show that the infinitesimal deformations of the Brill--Noether locus $W_d$ attached to a smooth non-hyperelliptic curve $C$ are in one-to-one correspondence with the deformations of $C$. As an application, we prove that if a Jacobian $J$…

We suggest that Bipolar H{\sc ii} Regions may be the aftermath of collisions between clouds. Such a collision will produce a shock-compressed layer, and a star cluster can then condense out of the dense gas near the centre of the layer. If…

An MBM class on a hyperkahler manifold M is a second cohomology class such that its orthogonal complement in H^2(M) contains a maximal dimensional face of the boundary of the Kahler cone for some hyperkahler deformation of M. An MBM curve…

The rational blowdown operation in 4-manifold topology replaces a neighborhood of a configuration of spheres by a rational homology ball. Such configurations typically arise from resolutions of surface singularities that admit rational…

For a K\"ahler manifold $X$ equipped with a prequantum line bundle $L$, we give a geometric construction of a family of representations of the Berezin-Toeplitz deformation quantization algebra $(C^\infty(X)[[\hbar]],\star_{BT})$…

We introduce a type of minimal surface in the pseudo-hyperbolic space $\mathbb{H}^{n,n}$ (with $n$ even) or $\mathbb{H}^{n+1,n-1}$ (with $n$ odd) associated to cyclic $\mathrm{SO}_0(n,n+1)$-Higg bundles. By establishing the infinitesimal…

Let $L$ be a compact oriented Lagrangian surface in a K\"ahler surface endowed with a complete Riemannian metric (compatible with the symplectic structure and the complex structure) with bounded sectional curvatures and a positive lower…

Shafarevich conjecture/problem is about the finiteness of isomorphism classes of a family of varieties defined over a number field with good reduction outside a finite collection of places. For K3 surfaces, such a finiteness result was…

We show that any dimension $6$ nearly K\"ahler (or nearly para-K\"ahler) geometry arises as a projective manifold equipped with a $\textrm{G}_2^{(*)}$ holonomy reduction. In the converse direction we show that if a projective manifold is…

We investigate the formal principle for holomorphic line bundles on neighborhoods of an analytic subset of a complex manifold mainly in the case where it can be realized as an open subset of a compact K\"ahler manifold. Our approach…

We establish a general `gluing theorem', which states roughly that if two nondegenerate constant mean curvature surfaces are juxtaposed, so that their tangent planes are parallel and very close to one another, but oppositely oriented, then…

Suppose $k$ is an algebraically closed field of characteristic two, let $A_4$ be an alternating group on four letters, and let $H$ be the unique Sylow two-subgroup of $A_4$. Let $X$ be a smooth projective irreducible curve over $k$ with a…

We continue the study of compact holomorphic $p$-contact manifolds $X$ that we introduced recently by expanding the discussion to include non-K\"ahler hyperbolicity issues and a differential calculus based on what we call the Lie derivative…