Related papers: Shadows of a Closed Curve

Shadow art is a captivating form of sculptural expression where the projection of a sculpture in a specific direction reveals a desired shape with high precision. In this work, we introduce Neural Shadow Art, which leverages implicit…

Let E/Q be an elliptic curve and p a rational prime of good ordinary reduction. For every imaginary quadratic field K/Q satisfying the Heegner hypothesis for E we have a corresponding line in E(K)\otimes Q_p, known as a shadow line. When…

We define shadowable points for homeomorphism on metric spaces. In the compact case we will prove the following results: The set of shadowable points is invariant, possibly nonempty or noncompact. A homeomorphism has the pseudo-orbit…

We estimate from below the number of lines meeting each of given 4 disjoint smooth closed curves in a given cyclic order in the real projective 3-space and in a given linear order in the Euclidean 3-space. Similarly, we estimate the number…

Let $S$ be a complete flat surface, such as the Euclidean plane. We obtain direct characterizations of the connected components of the space of all curves on $S$ which start and end at given points in given directions, and whose curvatures…

We show that shadowing is a generic property among continuous maps and surjections on a large class of locally connected one-dimensional continua.

We present the shape of the black hole shadow on the standard background screen as it is registered by the distant observer. The screen is an infinite plane, emitting the quanta uniformly distributed to a hemisphere. The source of emission…

Shadows encode rich information about scene geometry and illumination, yet existing methods either predict a unified shadow mask or overlook attached shadows entirely. We address this gap by proposing a framework for jointly detecting cast…

This article is about the shadowing property of homeomorphisms on compact metric spaces and the map associating a point of the space to each pseudo-orbit, called 'shadowing map'. Based on some particular dynamical properties, as…

An arrangement of pseudocircles $\mathcal{A}$ is a collection of Jordan curves in the plane that pairwise intersect (transversally) at exactly two points. How many non-equivalent links have $\mathcal{A}$ as their shadow? Motivated by this…

We study the set of all closed oriented smooth 4-manifolds experimentally, according to a suitable complexity defined using Turaev's shadows. This complexity roughly measures how complicated the 2-skeleton of the 4-manifold is. We…

We prove that the two-sided limit shadowing property is among the strongest known notions of pseudo-orbit tracing. It implies shadowing, average shadowing, asymptotic average shadowing and specification properties. We also introduce a…

We show that Euclidean geometry in suitably high dimension can be expressed as a theory of orthogonality of subspaces with fixed dimensions and fixed dimension of their meet.

According to a general definition of discrete curves, surfaces, and manifolds. This paper focuses on the Jordan curve theorem in 2D discrete spaces. The Jordan curve theorem says that a (simply) closed curve separates a simply connected…

In this paper we introduce congruence spaces, which are topological spaces that are canonically attached to monoid schemes and that reflect closed topological properties. This leads to satisfactory topological characterizations of closed…

Michael Shub proved in 1969 that the topological conjugacy class of an expanding endomorphism on a compact manifold is determined by its homotopy type. In this article we generalize this result in two directions. In one direction we…

The 1-form symmetries in two-dimensional topological systems are ``shadowed'' as global symmetries in their one-dimensional quantum transfer matrices. In this work, we introduce a distinct shadow effect arising from the pair-creation of…

In this paper, we employ a ray-tracing algorithm to simulate the shadows of three equal-mass black holes in static equilibrium across a wide parameter space. We find that the shadows consist of a larger primary shadow and several distorted,…

A distinct visual signature occurs in black holes that are surrounded by optically thin and geometrically thick emission regions. This signature is a sharp-edged dip in brightness that is coincident with the black-hole shadow, which is the…

A black hole embedded within a bright, optically thin emitting region imprints a nearly circular "shadow" on its image, corresponding to the observer's line-of-sight into the black hole. The shadow boundary depends on the black hole's mass…