Related papers: Partial immersions and partially free maps
In this expository manuscript, we review the construction of Gromov-Witten virtual fundamental class via FOOO's theory of Kuranishi structures for moduli spaces of pseudo-holomorphic maps defined on closed Riemann surfaces. We consider…
We provide a complete classification of the critical sets and their images for quadratic maps of the real plane. Critical sets are always conic sections, which provides a starting point for the classification. The generic cases, maps whose…
Let X be a minimal complex surface of general type such that its image via the canonical map is a surface; we denote by d the degree of the canonical map. In this expository work, first of all we recall the known possibilities for the…
Let M be a closed hyperbolic three manifold. We construct closed surfaces which map by immersions into M so that for each one the corresponding mapping on the universal covering spaces is an embedding, or, in other words, the corresponding…
A linear map between matrix spaces is positive if it maps positive semidefinite matrices to positive semidefinite ones, and is called completely positive if all its ampliations are positive. In this article quantitative bounds on the…
This paper is concerned with structures of general graphs with perfect matchings. We first reveal a partially ordered structure among factor-components of general graphs with perfect matchings. Our second result is a generalization of…
As a generalization of Riemannian submersions, horizontally conformal submersions, semi-invariant submersions, h-semi-invariant submersions, almost h-semi-invariant submersions, conformal semi-invariant submersions, we introduce h-conformal…
The asymptotic dimension is an invariant of metric spaces introduced by Gromov in the context of geometric group theory. When restricted to graphs and their shortest paths metric, the asymptotic dimension can be seen as a large scale…
Contact structures, as well as their holomorphic and quaternionic counterparts are the primary examples of strongly bracket generating (or fat) distributions. In this article we associate a numerical invariant to corank $2$ fat distribution…
We develop the foundations of the theory of quasi-visual approximations of bounded metric spaces. Roughly speaking, these are sequences of covers of a given space for which the diameters of the sets in the covers shrink to zero and for…
An immersion of a smooth $n$-dimensional manifold $M \to \mathbb{R}^q$ is called totally nonparallel if, for every distinct $x, y \in M$, the tangent spaces at $f(x)$ and $f(y)$ contain no parallel lines. Given a manifold $M$, we seek the…
In this paper we consider systems of partial (multidimensional) linear difference equations. Specifically, such systems arise in scientific computing under discretization of linear partial differential equations and in computational high…
In order to study the communication between information systems, Gong and Xiao [Z. Gong and Z. Xiao, Communicating between information systems based on including degrees, International Journal of General Systems 39 (2010) 189--206] proposed…
Let $ \B^{n+1} \subset \C^{n+1}$ be the unit ball in a complex Euclidean space, and let $ \Sigma^n = \partial \B^{n+1} = S^{2n+1}$. Let $ f: \Sigma^n \hook \Sigma^{N}$ be a local CR immersion.If $ N-n<2n-1$, the asymptotic vectors of the…
Completely positive trace preserving maps are widely used in quantum information theory. These are mostly studied using the master equation perspective. A central part in this theory is to study whether a given system of dynamical maps…
In this paper, we develop several tools to study the degree growth and stabilization of monomial maps. Using these tools, we can classify semisimple three dimensional monomial maps by their dynamical behavior.
We consider random labelings of finite graphs conditioned on a small fixed number of peaks. We introduce a continuum framework where a combinatorial graph is associated with a metric graph and edges are identified with intervals. Next we…
Geometric data and purpose-built generative models on them have become ubiquitous in high-impact deep learning application domains, ranging from protein backbone generation and computational chemistry to geospatial data. Current geometric…
The main objects under consideration in this thesis are called maps, a certain class of graphs embedded on surfaces. Our problems have a powerful relatively recent tool in common, the so-called topological recursion (TR) introduced by…
A $\bar{\partial}$-formalism for studying dispersionless integrable hierarchies is applied to the dKP hierarchy. Connections with the theory of quasiconformal mappings on the plane are described and some clases of explicit solutions of the…