Related papers: Equitable Mirrors
The eigenmirror problem asks: ``When does the reflection of a surface in a curved mirror appear undistorted to an observer?'' We call such a surface an {\em eigensurface} and the corresponding mirror an {\em eigenmirror}. The data for an…
We prove new Alexandrov-Fenchel type inequalities and new affine isoperimetric inequalities for mixed $p$-affine surface areas. We introduce a new class of bodies, the illumination surface bodies, and establish some of their properties. We…
In this paper we outline a setup for Homological Mirror Symmetry for manifolds of general type. Both Physics and Categorical perspectives are considered.
We study the effect of mirror symmetry for K3 surfaces on D-brane probe physics. The case of elliptically fibered K3 surfaces is considered in detail. In many cases, mirror can transform a singular fiber of Kodaira's type ADE into sets of…
We classify complete biharmonic surfaces with parallel mean curvature vector field and non-negative Gaussian curvature in complex space forms.
Optically resonant particles are key building blocks of many nanophotonic devices such as optical antennas and metasurfaces. Because the functionalities of such devices are largely determined by the optical properties of individual…
The traditional wisdom for achieving transparency is to minimize disordered scattering within and on the surface of materials, so as to avoid translucency. However, the lack of disordered scattering also deprives the possibility of…
This is the first in a series of papers where we develop new structural elements on singular area minimizing hypersurfaces, the skin structures. They disclose previously unapproachable and largely unexpected geometric and analytic…
Motivated by mirror symmetry for weighted projective spaces, we give a new characterization of exceptionoal unimodal singularities.
The design of new low-mechanical-loss, high reflectivity mirrors is crucial in the development of the next generation of gravitational-wave observatories. Currently, the state-of-the-art amorphous multilayer reflective coatings which are…
Metasurfaces enable efficient manipulation of electromagnetic radiation. In particular, control over plane-wave reflection is one of the most useful features in many applications. Extensive research has been done in the field of anomalous…
Chirality, handedness, is one of the most fundamental intriguing asymmetries in nature. By definition, chiral objects cannot be superimposed onto each other after mirror reflection operation. Numerous examples of chiral structures can be…
In this paper, we partially extend recent results of Wan concerning the relationship between the zeta functions of a Calabi-Yau hypersurface and its (singular) mirror variety.
Adaptive optics (AO) offers an opportunity to stabilize an image and maximize the spatial resolution achievable by ground based telescopes by removing the distortions due to the atmosphere. Typically, the deformable mirror in an AO system…
The kinematics of many mechanical systems encountered in robotics and other fields, such as single-bearing attitude estimation and SLAM, are naturally posed on homogeneous spaces: That is, their state lies in a smooth manifold equipped with…
In this paper induced U-equivalence spaces are introduced and discussed. Also the notion of U-equivalently open subsets of a U-equivalence space and U-equivalently open functions are studied. Finally, equivalently uniformisable topological…
In the present paper we establish some new integral inequalities analogous to the well known Hadamard inequality by using a fairly elementary analysis.
We present a reduction of codimension theorem for surfaces with parallel mean curvature in symmetric spaces.
Based on the concept of complementary media, we propose a novel design which can enhance the electromagnetic wave scattering cross section of an object so that it looks like a scatterer bigger than the scale of the device. Such a…
In this paper we study Seidel's mirror map for abelian and Kummer surfaces. We find that mirror symmetry leads in a very natural way to the classical parametrization of Kummer surfaces in $\P^3$. Moreover, we describe a family of embeddings…