相关论文: Calabi-Yau Problem for Legendrian curves in C^3 an…
In this paper we study holomorphic immersions of open Riemann surfaces into C^n whose derivative lies in a conical algebraic subvariety A of C^n that is smooth away from the origin. Classical examples of such A-immersions include null…
We construct Calabi-Yau 3-folds as orbifolds embedded in weighted projective space in codimension 4. For each Hilbert series that is realised, there are at least two different components of Calabi-Yau 3-folds.
We introduce a local coordinate description for the correspondence between the space of oriented affine lines in Euclidean ${\Bbb{R}}^3$ and the tangent bundle to the 2-sphere. These can be utilised to give canonical coordinates on surfaces…
In this short note we apply methods of Aspinwall-Katz to compute superpotentials of D-branes wrapped on more general obstructed rational curves in Calabi-Yau threefolds. We find an a priori unexpected match between superpotentials from…
In an earlier paper, we proved that, under certain hypotheses, the moduli space of an asymptotically cylindrical special Lagrangian submanifold with fixed boundary of an asymptotically cylindrical Calabi-Yau 3-fold is a smooth manifold.…
Let $X$ be either a general hypersurface of degree $n+1$ in $\mathbb P^n$ or a general $(2,n)$ complete intersection in $\mathbb P^{n+1}, n\geq 4$. We construct balanced rational curves on $X$ of all high enough degrees. If $n=3$ or $g=1$,…
We prove existence of thick geodesic triangulations of hyperbolic 3-manifolds and use this to prove existence of universal bounds on the principal curvatures of surfaces embedded in hyperbolic 3-manifolds.
Every closed, oriented, real analytic Riemannian 3-manifold can be isometrically embedded as a special Lagrangian submanifold of a Calabi-Yau 3-fold, even as the real locus of an antiholomorphic, isometric involution. Every closed,…
We describe the space of isometric immersions from the Lorentz plane $L^2$ into the 3-dimensional anti-de Sitter space, and solve several open problems of this context raised by M. Dajczer and K. Nomizu in 1981. We also obtain from the…
We study threefolds fibred by Kummer surfaces associated to products of elliptic curves, that arise as resolved quotients of threefolds fibred by certain lattice polarized K3 surfaces under a fibrewise Nikulin involution. We present a…
We introduce a new formalism and a number of new results in the context of geometric computational vision. The classical scope of the research in geometric computer vision is essentially limited to static configurations of points and lines…
The purpose of this paper is to prove a gluing theorem for a given special Lagrangian submanifold of a Calabi-Yau 3-fold. The proof will be an adaption of the gluing techniques in J-holomorphic curve theory. It is a well known procedure in…
We determine all the Kummer-surface-type Calabi-Yau (CY) 3-folds, i.e., those $\hat{T/G}$ which are resolutions of 3-torus-orbifolds $T/G$ with only isolated singularities. There are only two such CY spaces: one with $G= \ZZ_3$ and $T$…
This work deals with the study of embeddings of toric Calabi-Yau fourfolds which are complex cones over the smooth Fano threefolds. In particular, we focus on finding various embeddings of Fano threefolds inside other Fano threefolds and…
In this article we provide a general construction when $n\ge3$ for immersed in Euclidean $(n+1)$-space, complete, smooth, constant mean curvature hypersurfaces of finite topological type (in short CMC $n$-hypersurfaces). More precisely our…
In this article we study Weinstein structures endowed with a Lefschetz fibration in terms of the Legendrian front projection. First we provide a systematic recipe for translating from a Weinstein Lefschetz bifibration to a Legendrian…
We study positivity-preserving properties for the elastic flow of non-compact, complete curves in Euclidean space. Despite the fact that the canonical elastic energy is infinite in this context, we extend our recent work based on the…
We formulate a version of the integral Hodge conjecture for categories, prove the conjecture for two-dimensional Calabi-Yau categories which are suitably deformation equivalent to the derived category of a K3 or abelian surface, and use…
We study threefolds fibred by K3 surfaces admitting a lattice polarization by a certain class of rank 19 lattices. We begin by showing that any family of such K3 surfaces is completely determined by a map from the base of the family to the…
We consider non-compact Calabi-Yau threefolds that are fibrations over compact Riemann surfaces, the local curves, and study the dynamics of B-branes wrapped around the curves. We discuss different but closely related possible approaches to…