Related papers: Meromorphic quadratic differentials and measured f…

We construct an example of a uniquely ergodic measured foliation on a surface such that the associated translation flow on the orientation double cover is minimal but not uniquely ergodic. We then prove a geometric criterion for the…

Let $(M,g)$ be a 3-dimensional Riemannian manifold. The goal of the paper it to show that if $P_{0}\in M$ is a non-degenerate critical point of the scalar curvature, then a neighborhood of $P_{0}$ is foliated by area-constrained Willmore…

In this paper, we analyze the theory of meromorphic $(1,0)$-forms $\omega\in\mathcal{M}\Omega^{(1,0)}(\mathbb{CP}^1).$ Hence, we show that on a compact Riemann surface of genus $g=0,$ isomorphic to $\mathbb{CP}^1,$ every non-constant…

We give an easy example showing that sections of a singular Riemannian foliation on a simply connected space neither have to be isometric nor injectively immersed.

Extremal length is an important conformal invariant on Riemann surface. It is closely related to the geometry of Teichmuller metric on Teichmuller space. By identifying extremal length functions with energy of harmonic maps from Riemann…

The Separatrix Theorem of C. Camacho and P. Sad guarantees the existence of invariant curve (separatrix) passing through the singularity of germ of holomorphic foliation on complex surface, when the surface underlying the foliation is…

Yu. I. Manin conjectured that the maximal abelian extensions of the real quadratic number fields are generated by the pseudo-lattices with real multiplication. We prove this conjecture using theory of measured foliations on the modular…

A singular riemannian foliation on a complete riemannian manifold is said to be riemannian if each geodesic that is perpendicular at one point to a leaf remains perpendicular to every leaf it meets. The singular foliation is said to admit…

A theorem about local in time existence of spacelike foliations with prescribed mean curvature in cosmological spacetimes will be proved. The time function of the foliation is geometrically defined and fixes the diffeomorphism invariance…

A new notion of cohomology is introduced for MT-spaces, which are measurable and topological spaces whose measurable structure may not agree with the Borel $\sigma$-algebra of their topology. The main examples of MTspaces are measurable…

Following Zagier, this work studies the rationality and divisibility of Fourier coefficients of meromorphic Hilbert modular forms associated with real quadratic fields, using theta lifts and weak Maass forms. We establish conditions where…

We prove that moduli spaces of meromorphic quadratic differentials with simple zeroes on compact Riemann surfaces can be identified with spaces of stability conditions on a class of CY3 triangulated categories defined using quivers with…

Masur showed that a Teichmuller geodesic that is recurrent in the moduli space of closed Riemann surfaces is necessarily determined by a quadratic differential with a uniquely ergodic vertical foliation. In this paper, we show that a…

Two measurable sets $S, \Lambda \subseteq \mathcal{R}^d$ form a Heisenberg uniqueness pair, if every bounded measure $\mu$ with support in S whose Fourier transform vanishes on {\Lambda} must be zero. We show that a quadratic hypersurface…

It is known that spherically symmetric static spacetimes admit a foliation by {\deg}at hypersurfaces. Such foliations have explicitly been constructed for some spacetimes, using different approaches, but none of them have proved or even…

In this paper, we develop $L^2$ theory for Riemannian and Hermitian foliations on manifolds with basic boundary. We establish a decomposition theorem, various vanishing theorems, a twisted duality theorem for basic cohomologies and an…

This paper, which is an outgrowth of a previous paper of the authors, continues the study of dimension 1 foliations on non-metrisable manifolds emphasising some anomalous behaviours. We exhibit surfaces with various extra properties like…

A practical method is presented for determining root and pole cancellation functions of a matrix function $Q(z)$ meromorphic on the extended complex plane $\bar{\mathbb{C}}:=\mathbb{C} \cup \left\{ \infty \right\}$. This method is applied…

It is well known that, by the Reeb stability theorem, the leaf space of a Riemannian foliation with compact leaves is an orbifold. We prove that, under mild completeness conditions, the leaf space of a Killing Riemannian foliation is a…

We consider the class of compact Riemann surfaces which are ramified coverings of the Riemann sphere $\hat{\mathbb{C}}$. Based on a triangulation of this covering of the sphere $\mathbb{S}^2\cong \hat{\mathbb{C}}$ and its stereographic…