Related papers: Bodies invisible from one point

In this paper we classify those three-dimensional Riemannian Lie groups which admit harmonic morphisms to surfaces.

We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group G, focusing on surfaces without marked points or with one marked point. We obtain concrete descriptions of…

We present a computational framework that transforms single images into 3D physical objects. The visual geometry of a physical object in an image is determined by three orthogonal attributes: mechanical properties, external forces, and…

We exhibit automorphisms of a certain K3 surface in $\mathbb{P}^1\times \mathbb{P}^1 \times \mathbb{P}^1$ with an isolated fixed point at which the induced action on the stalk of the structure sheaf is arbitrarily close to the identity.…

We introduce complex intersection bodies and show that their properties and applications are similar to those of their real counterparts. In particular, we generalize Busemann's theorem to the complex case by proving that complex…

We consider the problem of camouflaging for bodies with specular surface in the framework of geometric optics. The index of visibility introduced in [Plakhov 2017] measures the mean deviation of light rays incident on the body's surface. We…

Some intensive observables of the electronic ground state in condensed matter have a geometrical or even topological nature. In this Review I present the geometrical observables whose expression is known in a full many-body framework,…

We consider various problems related to finding points in $\Q^{2}$ and in $\Q^{3}$ which lie at rational distance from the vertices of some specified geometric object, for example, a square or rectangle in $\Q^{2}$, and a cube or…

In this paper, we mainly introduce the notion of an open uniform (G) at non-isolated points, and show that a space $X$ has an open uniform (G) at non-isolated points if and only if $X$ is the open boundary-compact image of metric spaces.…

General relativity includes geometrical optics. This basic fact has relevant consequences that concern the physical meaning of the discontinuity surfaces propagated in the gravitational field - as it was first emphasized by Levi-Civita.

There are three complete plane geometries of constant curvature: spherical, Euclidean and hyperbolic geometry. We explain how a closed oriented surface can carry a geometry which locally looks like one of these. Focussing on the hyperbolic…

With the present and soon-to-be breakthrough of optical interferometry, countless objects shall be within reach of interferometers; yet, most of them are expected to remain only marginally resolved with hectometric baselines. In this paper,…

We propose to use transformation optics to generate a general illusion such that an arbitrary object appears to be like some other object of our choice. This is achieved by using a remote device that transforms the scattered light outside a…

While there is extensive literature on approximation of convex bodies by inscribed or circumscribed polytopes, much less is known in the case of generally positioned polytopes. Here we give upper and lower bounds for approximation of convex…

It is shown that the geometrical optics limit of the Maxwell equations for certain nonlinear media with slow variation along one axis and particular dependence of dielectric constant on the frequency and fields gives rise to the…

We give an infinite presentation for the mapping class group of a non-orientable surface with boundary components. The presentation is a generalization of the presentation given by the second author [15].

We find conditions under which a non-orientable closed surface S embedded into an orientable closed 4-manifold X can be represented by a connected sum of an embedded closed surface in X and an unknotted projective plane in a 4-sphere. This…

A problem that is simple to state in the context of spherical geometry, and that seems rather interesting, appears to have been unexamined to date in the mathematical literature. The problem can also be recast as a problem in the real…

We investigate geometrical properties and inequalities satisfied by the complex difference body, in the sense of studying which of the classical ones for the difference body have an analog in the complex framework. Among others we give an…

A representation of a finitely generated group into the projective general linear group is called convex co-compact if it has finite kernel and its image acts convex co-compactly on a properly convex domain in real projective space. We…