arXiv research

Let $M$ be a Riemannian manifold. For $p\in M$, the tensor algebra of the negative part of the (complex) affinization of the tangent space of $M$ at $p$ has a natural structure of a meromorphic open-string vertex algebra. These meromorphic open-string vertex algebras form a vector bundle over $M$ with a connection. We …

Study the geometry of twistor spaces with rotating circle action.

The paper studies deformations of Lagrangian fibrations on symplectic manifolds.

Study meromorphic open-string vertex algebras and modules over Riemannian manifolds.

Study of symplectic groupoids from tt*-Toda equations.

In this note, we study the dynamics and associated zeta functions of conformally compact manifolds with variable negative sectional curvatures. We begin with a discussion of a larger class of manifolds known as convex co-compact manifolds with variable negative curvature. Applying results from dynamics on these spaces,…

A (meromorphic) quadratic differential is a (meromorphic) section of the tensor square of the canonical bundle of a Riemann surface. They arose in the study of quasiconformal mappings in the works of Oswald Teichmüller, and have played a mayor role in the study of the Riemann moduli, where they can be identified with c…

We study a natural functional on the space of holomorphic sections of the Deligne-Hitchin moduli space of a compact Riemann surface, generalizing the energy of equivariant harmonic maps corresponding to twistor lines. We give a link to a natural meromorphic connection on the hyperholomorphic line bundle recently constr…

A new projective structure on Riemann surfaces differs from the uniformization theorem's structure.

A Kleinian manifold Y is a quotient of a rank-one symmetric space of non-compact type by a convex-cocompact discrete group of isometries. We describe the spectral decomposition of the space of square integrable sections of locally homogeneous bundles on Y with respect to locally invariant differential operators. In the…

We study special circle bundles over two elementary moduli spaces of meromorphic quadratic differentials with real periods denoted by $\mathcal Q_0^{\mathbb R}(-7)$ and $\mathcal Q^{\mathbb R}_0([-3]^2)$. The space $\mathcal Q_0^{\mathbb R}(-7)$ is the moduli space of meromorphic quadratic differentials on the Riemann …

This paper extends Nevanlinna's unicity theorems to complete Kahler manifolds.

Study projective flat vector bundles over Riemann surfaces using Wronskian line bundles.

The spinor representation is developed for conformal immersions of Riemann surfaces into space. We adapt the approach of Dennis Sullivan, which treats a spin structure on a Riemann surface M as a complex line bundle S whose square is the canonical line bundle K=T(M). Given a conformal immersion of M into \bbR^3, the un…

Study describes how to realize periods of meromorphic differentials with specific properties.

Study of twistor spaces and minitwistor spaces for ALE gravitational instantons.

The paper studies the distribution of random degeneracy sets on complex manifolds.

Study geodesics of meromorphic connections on Riemann surfaces.

Constructs a function to prove meromorphic differential strata don't have complete subvarieties.

This paper classifies components of meromorphic differential strata.

Classifies meromorphic affine connections on complex surfaces.

Study rationality of meromorphic functions between real algebraic sets in the plane.

Classifies connected components of meromorphic differentials with residue conditions.

The paper studies complex affine structures near irregular singularities.

The paper explores meromorphic connections over Frobenius manifolds.

The paper studies deformations and confluences of singularities in meromorphic connections and quadratic differentials.

Classifies Teichmüller curves in specific hyperelliptic components of meromorphic differentials.

This work is based on the approach developed by J.~Dorfmeister, F.~Pedit and H.~Wu [GANG and KITCS preprint, Report KITCS94-4-1] to construct maps $Φ:D\rightarrow R^3$, $D$ being the unit disk in $C$, whose images are surfaces of constant mean curvature. They start from certain meromorphic one forms, so called meromorp…

Using the locally compact abelian group $\BT \times \BZ$, we assign a meromorphic function to each ideal triangulation of a 3-manifold with torus boundary components. The function is invariant under all 2--3 Pachner moves, and thus is a topological invariant of the underlying manifold. If the ideal triangulation has a …

Researchers compute the index of meromorphic functions on tori.

Abstract framework for two meromorphic forms on punctured surfaces.

We study the local Killing Lie algebra of meromorphic almost rigid geometric structures on complex manifolds. This leads to classification results for compact complex manifolds bearing holomorphic rigid geometric structures.

A meromorphic projective structure on a punctured Riemann surface $X\setminus P$ is determined, after fixing a standard projective structure on $X$, by a meromorphic quadratic differential with poles of order three or more at each puncture in $P$. In this article we prove the analogue of Thurston's grafting theorem for…

This paper explores how local behavior of meromorphic connections on the projective line determines the global connection.

The paper explores anti-hyperbolicity for hyperkähler varieties.

The study characterizes a complex curve of residueless meromorphic differentials on elliptic curves.

Study linear subvarieties of meromorphic differential strata, proving toric closures and new proofs of theorems.

We extend Vasy's results on semiclassical high energy estimates for the meromorphic continuation of the resolvent for asymptotically hyperbolic manifolds to metrics that are not necessarily even. Vasy's method gives the meromorphic continuation of the resolvent and high energy estimates in strips, assuming that the geo…

Geometric approach to meromorphic differentials' periods and their holonomy representations.

Normal forms found for meromorphic connections over a specific F-manifold.

Pólya's theorem extended to meromorphic functions on Riemann surfaces.

Study meromorphic k-differentials with prescribed singularities on Riemann surfaces.

We consider those simply connected isothermic surfaces for which their Hopf differential factorizes into a real function and a meromorphic quadratic differential that has a zero or pole at some point, but is nowhere zero and holomorphic otherwise. Upon restriction to a simply connected patch that does not contain the z…

The paper defines and computes volumes of meromorphic differentials with simple poles.

In analogy with the holomorphic case, we compare the topology of Milnor fibrations associated to a meromorphic germ f/g : the local Milnor fibrations given on Milnor tubes over punctured discs around the critical values of f/g, and the Milnor fibration on a sphere.

A meromorphic quadratic differential on a punctured Riemann surface induces horizontal and vertical measured foliations with pole-singularities. In a neighborhood of a pole such a foliation comprises foliated strips and half-planes, and its leaf-space determines a metric graph. We introduce the notion of an asymptotic …

The Mittag-Leffler theorem is extended to meromorphic curves and minimal surfaces.

One-parameter smooth families of circles in the complex plane with the following property are described: a function is polyanalytic if and only if it has meromorphic extension inside any circle from the family, with the only singularity-a pole at the center.