Related papers: Bergman completeness is not a quasi-conformal inva…
We prove a heat semigroup characterization of the total variation for compactly supported ${\rm BV}$ on arbitrary smooth complete weighted Riemannian manifolds, extending the main result in \cite{GP15}. We then provide an example of a…
The existence of closed hypersurfaces of prescribed curvature in semi-riemannian manifolds is proved provided there are barriers.
This article is a survey of results involving conformal deformation of Riemannian metrics and fully nonlinear equations.
We state and prove a corrected version of a theorem of Singerman, which relates the existence of symmetries (anticonformal involutions) of a quasiplatonic Riemann surface $\mathcal S$ (one uniformised by a normal subgroup $N$ of finite…
We establish a uniformization result for metric surfaces - metric spaces that are topological surfaces with locally finite Hausdorff 2-measure. Using the geometric definition of quasiconformality, we show that a metric surface that can be…
We show that every open Riemann surface can be obtained by glueing together a countable collection of equilateral triangles, in such a way that every vertex belongs to finitely many triangles. Equivalently, it is a _Belyi surface_: There…
We demonstrate the existence of quasiconformal mappings on closed manifolds that cannot be decomposed as a composition of mappings with arbitrarily small conformal distortion.
As a generalization of anti-invariant $\xi^\perp-$Riemannian submersions, we introduce conformal anti-invariant $\xi^\perp-$submersions from almost contact metric manifolds onto Riemannian manifolds. We investigate the geometry of…
We show that the fundamental group is not invariant under derived equivalence of smooth projective varieties.
The present paper is devoted to the study of mappings with finite distortion on Riemannian manifolds. Theorems on local behavior of generalized quasiisometries with unbounded characteristic of quasiconformality are obtained.
We prove that every Riemann surface not isomorphic to the Riemann sphere admits an infinitesimal deformation of the complex structure. The proof is based in an investigation of the length of geodesics for the Kobayashi/Poincare metric.
We consider a compact Riemann surface $R$ of arbitrary genus, with a finite number of non-overlapping quasicircles, which separate $R$ into two subsets: a connected Riemann surface $\Sigma$, and the union $\mathcal{O}$ of a finite…
We construct a complete Riemannian surface $\Sigma$ that admits no triangulation $G\subset \Sigma$ such that the inclusion $G^{(1)} \hookrightarrow \Sigma$ is a quasi-isometry, where $G^{(1)}$ is the simplicial 1-skeleton of $G$. Our…
We give a proof that the Riemann hypothesis for hypersurfaces over finite fields implies the result for all smooth proper varieties, by a deformation argument which does not use the theory of Lefschetz pencils or the l-adic Fourier…
It is an open problem to provide a characterization of quasiconformally homogeneous Riemann surfaces. We show that given the current literature, this problem can be broken into four open cases with respect to the topology of the underlying…
In this paper, we obtain the isoperimetric inequality on conformally flat manifold with finite total $Q$-curvature. This is a higher dimensional analogue of Li and Tam's result \cite{L-T} on surfaces with finite total Gaussian curvature.…
We consider the Bergman space on the complex plane. We prove an analogue of Schwarz's reflection principle for unbounded quasidisks.
The purpose of this paper is to study anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds. Several fundamental results in this respect are proved. The integrability of the distributions and the geometry…
We introduce the notion of a conformal de Rham complex of a Riemannian manifold. This is a graded differential Banach algebra and it is invariant under quasiconformal maps, in particular the associated cohomology is a new quasiconformal…
We prove that if a complete Riemannian surface $(\Sigma,d_\Sigma)$ is quasi-isometric to some bounded degree graph $G$, then $\Sigma$ admits a triangulation whose 1-skeleton is quasi-isometric to it when equipped with the simplicial metric.…