Related papers: Isometric immersions and applications

Applications of Integrated Optics to quantum sources, detectors, interfaces, memories and linear optical quantum computing are described in this review. By their inherent compactness, efficiencies, and interconnectability, many of the…

We give a simple rigourous treatment of the classical results of the abelian sandpile model. Although we treat results which are well-known in the physics literature, in many cases we did not find complete proofs in the literature. The…

Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…

Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…

It is shown that any bounded metric space can be isometrically embedded into the Gromov--Hausdorff metric class GH. This result is a consequence of local geometry description of the class GH in a sufficiently small neighborhood of a generic…

We define virtual immersions, as a generalization of isometric immersions in a pseudo-Riemannian vector space. We show that virtual immersions possess a second fundamental form, which is in general not symmetric. We prove that a manifold…

The notion of geometric version of an infinitely divisible law is introduced. Concepts parallel to attraction and partial attraction are developed and studied in the setup of geometric summing of random variables.

This book is addressed to students, professors and researchers of geometry, who will find herein many interesting and original results. The originality of the book The Geometry of Homological Triangles consists in using the homology of…

A proof of the isometric embedding of a given two-metric in E^3 of class C^1. The method uses the theory of first order partial differential equations. The curvature of the metric plays no role in the proof.

This work is devoted to study the deformation of spacetime metrics as generalized conformal transformations. Some applications are also considered, in particular the equations of motion in deformed spacetime are studied.

This work provides a thorough introduction to the field of gammoids and presents new results that are considered helpful for solving the problems of recognizing and coloring gammoids.

The concept of quasi-isometric embedding maps between $*$-algebras is introduced. We have obtained some basic results related to this notion and similar to quasi-isometric embedding maps on metric spaces, under some conditions, we give a…

When matching parts of a surface to its whole, a fundamental question arises: Which points should be included in the matching process? The issue is intensified when using isometry to measure similarity, as it requires the validation of…

We apply an old method for constructing points-and-lines configurations in the plane to study some recent questions in incidence geometry.

We describe the duality between different geometries which arises by considering the classical and quantum harmonic map problem. To appear in ``Essays on Mirror Manifolds II''.

Quadrilateral layouts on surfaces are valuable in texture mapping, and essential in generation of quadrilateral meshes and in fitting splines. Previous work has characterized such layouts as a special metric on a surface or as a meromorphic…

We survey recent progress in the study of flows of isometric $G_2$-structures on 7-dimensional manifolds, that is, flows that preserve the metric, while modifying the $G_2$-structure. In particular, heat flows of isometric $G_2$-structures…

In this paper we make an overview of results relating the recent "discoveries" in differential geometry, such as higher structures and differential graded manifolds with some natural problems coming from mechanics. We explain that a lot of…

We recall the question of geometric integrators in the context of Poisson geometry, and explain their construction. These Poisson integrators are tested in some mechanical examples. Their properties are illustrated numerically and they are…

We survey some recent applications of machine learning to problems in geometry and theoretical physics. Pure mathematical data has been compiled over the last few decades by the community and experiments in supervised, semi-supervised and…