Related papers: Domes over curves

A classification of discrete integrable systems on quad-graphs, i.e. on surface cell decompositions with quadrilateral faces, is given. The notion of integrability laid in the basis of the classification is the three-dimensional…

We prove that any geometrically connected curve $X$ over a field $k$ is an algebraic $K(\pi,1)$, as soon as its geometric irreducible components have nonzero genus. This means that the cohomology of any locally constant constructible…

Graham Theorem on the unit ball $B_{n}$ in $\mathbb{C}^{n}$ states that every invariant harmonic function $u\in C^{n}(\overline{B}_{n})$ must be pluriharmonic in $B_{n}$. This rigidity phenomenon of Graham have been studied by many authors.…

The main goal of this paper is to investigate the minimal size of families of curves on surfaces with the following property: a family of simple closed curves $\Gamma$ on a surface realizes all types of pants decompositions if for any pants…

We give upper bounds on the genus of a curve with general moduli assuming that it can be embedded in a projective nonsingular surface $Y$ so that $\dim(|C|) > 0$. We find such bounds for all types of surfaces of intermediate Kodaira…

We show the existence of metrically dense entire curves in rationally connected complex projective manifolds confirming for this case a conjecture according to which such entire curves on projective manifolds exist if and only if these are…

Let $f$ be a plane curve. We give a procedure based on Abhyankar's approximate roots to detect if it has a single place at infinity, and if so construct its associated $\delta$-sequence, and consequently its value semigroup. Also for fixed…

This talk reviews recent developments in the field of analytical Feynman integral calculations. The central theme is the geometry associated to a given Feynman integral. In the simplest case this is a complex curve of genus zero (aka the…

We consider curves $\gamma : [0, 1]\to\mathbb{R}^3$ endowed with an adapted orthonormal frame $r : [0, 1]\to SO(3)$. We are interested in the cases where the frame is constrained, in the sense that one of its `curvatures' (i.e.,…

In this article, we first show that for all compact Riemannian manifolds with non-empty smooth boundary and dimension at least 3, there exists a metric, pointwise conformal to the original metric, with constant scalar curvature in the…

A linear system on a smooth complex algebraic surface gives rise to a family of smooth curves in the surface. Such a family has a topological monodromy representation valued in the mapping class group of a fiber. Extending arguments of…

We prove that a smooth, complex plane curve $C$ of odd degree can be defined by a polynomial with real coefficients if and only if $C$ is isomorphic to its complex conjugate. Counterexamples are known for curves of even degree. More…

Let $\Gamma$ be an arrangement of Jordan curves in the plane, i.e., simple closed curves in the plane. For any curve $\gamma \in \Gamma$, we denote the bounded region enclosed by $\gamma$ as $\tilde{\gamma}$. We say that $\Gamma$ is…

Let $M$ be a graph manifold such that each piece of its JSJ decomposition has the $\Bbb H^2 \times \Bbb R$ geometry. Assume that the pieces are glued by isometries. Then, there exists a complete Riemannian metric on $\Bbb R \times M$ which…

A monotone cylindrical graph is a topological graph drawn on an open cylinder with an infinite vertical axis satisfying the condition that every vertical line intersects every edge at most once. It is called simple if any pair of its edges…

We introduce new families of quandles that serve as invariants for classifying closed orientable surfaces. These families generalize the classical Dehn quandle and are defined, respectively, on isotopy classes of unoriented closed curves…

In 2007 Phillips and Weaver showed that, assuming the Continuum Hypothesis, there exists an outer automorphism of the Calkin algebra. (The Calkin algebra is the algebra of bounded operators on a separable complex Hilbert space, modulo the…

Any smooth projective curve embeds into $\mathbb{P}^3$. More generally, any curve embeds into a rationally connected variety of dimension at least three. We prove conversely that if every curve embeds in a threefold $X$, then $X$ is…

In this article we discuss classical theorems from Convex Geometry in the context of topological drawings and beyond. In a simple topological drawing of the complete graph $K_n$, any two edges share at most one point: either a common vertex…

We study the weighted integral transform on a compact manifold with boundary over a smooth family of curves $\Gamma$. We prove generic injectivity and a stability estimate under the condition that the conormal bundle of $\Gamma$ covers…