Related papers: On pseudo-Anosov mapping classes with minimum dila…

We introduce the notion of translational Riemannian manifolds and define a Gauss map for orientable immersed hypersurfaces lying in these ambients, an associated translational curvature and prove a Gauss-Bonnet theorem. We also use this…

Let $S$ be a minimal compact complex surface with Betti numbers $b_1(S)=1$ and $b_2(S)\ge 1$ i.e. a compact surface in class VII$_0^+$. We show that if there exists a twisted logarithmic 1-form $\tau\in H^0(S,\Omega^1(\log D)\otimes…

It is a well known phenomenon that many classical minimal surfaces in Euclidean space also exist with higher dihedral symmetry. More precisely, these surfaces are solutions to free boundary problems in a wedge bounded by two vertical planes…

Let $M$ be an $n$-dimensional manifold supporting a quasi Anosov diffeomorphism. If $n=3$ then either $M={\mathbb T}^3$, in which case the diffeomorphisms is Anosov, or else its fundamental group contains a copy of ${\mathbb Z} ^6$. If…

For $\Omega \subset \mathbb{R}^n$, a convex and bounded domain, we study the spectrum of $-\Delta_\Omega$ the Dirichlet Laplacian on $\Omega$. For $\Lambda\geq0$ and $\gamma \geq 0$ let $\Omega_{\Lambda, \gamma}(\mathcal{A})$ denote any…

Using techniques of deformation (bi)quantization we establish a non-canonical algebra isomorphism between the deformed reduction algebra and the invariant differential operators on G/H. Further results concerning other deformations of these…

In the 1960s Arnold conjectured that a Hamiltonian diffeomorphism of a closed connected symplectic manifold $(M,\omega)$ should have at least as many contractible fixed points as a smooth function on $M$ has critical points. Such a…

Let $S$ be a Riemann surface with a puncture $x$. Let $a\subset S$ be a simple closed geodesic. In this paper, we show that for any pseudo-Anosov map $f$ of $S$ that is isotopic to the identity on $S\cup \{x\}$, $(a, f^m(a))$ fills $S$ for…

We extend the celebrated theorem of Kellogg for conformal diffeomorphisms to the minimizers of Dirichlet energy. Namely we prove that a diffeomorphic minimiser of Dirichlet energy of Sobolev mappings between doubly connected Riemanian…

Let $D$ be a digraph of order $n$ with adjacency matrix $A(D)$. For $\alpha\in[0,1)$, the $A_{\alpha}$ matrix of $D$ is defined as $A_{\alpha}(D)=\alpha {\Delta}^{+}(D)+(1-\alpha)A(D)$, where…

In this note, we use a result of Osserman and Schiffer \cite{OS} to give a variational characterization of the catenoid. Namely, we show that subsets of the catenoid minimize area within a geometrically natural class of minimal annuli. To…

A dichotomous ordinal graph consists of an undirected graph with a partition of the edges into short and long edges. A geometric realization of a dichotomous ordinal graph $G$ in a metric space $X$ is a drawing of $G$ in $X$ in which every…

In this article, we prove that if $(M,g)$ is a genus $G$ orientable surface with a single boundary component $S^1$, and if $(D,g_0)$ is a disc such that interior points are connected by unique geodesics and $$d_{(D,g_0)}(x,y) \geq…

A well known theorem in graph theory states that every graph $G$ on $n$ vertices and minimum degree at least $d$ contains a path of length at least $d$, and if $G$ is connected and $n\ge 2d+1$ then $G$ contains a path of length at least…

The degree of a map between orientable manifolds is a fundamental concept in topology, providing deep insights into the structure of manifolds and the behavior of maps between them. Recently, this notion has been extensively studied,…

The objects of study are triangulations of the dilated standard triangle in the plane. Motivated by work on T-curves (Geiselmann et al., 2026), the focus lies on unimodular triangulations with a fixed symmetry axis. Lower and upper bounds…

Let $\mathcal{C}$ be the family of compact convex subsets $S$ of the hemisphere in $\rn$ with the property that $S$ contains its dual $S^*;$ let $u\in S^*$, and let $ \Phi(S,u)=\frac{2}{\omega_n}\int_{S}\ < \theta, u \ > \,\,…

Let $G$ be a unipotent group and $\mathcal F=\{F_t:t\in (0,\infty)\}$ a family of subsets of $G$, with $\mathcal F$ definable in an o-minimal expansion of the real field. Given a lattice $\Gamma\subseteq G$, we study the possible Hausdorff…

This paper compares the divisorial gonality of a finite graph $G$ to the divisorial gonality of the associated metric graph $\Gamma(G,\mathbb{1})$ with unit lengths. We show that $\text{dgon}(\Gamma(G,\mathbb{1}))$ is equal to the minimal…

We construct harmonic diffeomorphisms from the complex plane $C$ onto any Hadamard surface $M$ whose curvature is bounded above by a negative constant. For that, we prove a Jenkins-Serrin type theorem for minimal graphs in $M\times R$ over…