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This article is a local analysis of integrable GL(2)-structures of degree 4. A GL(2)-structure of degree n corresponds to a distribution of rational normal cones over a manifold M of dimension (n+1). Integrability corresponds to the…

Differential Geometry · Mathematics 2010-10-29 Abraham D. Smith

We consider in detail the structure of quartic vertices for massless higher spin fields on Minkowski background, and study the consistency conditions imposed on cubic and quartic interactions by symmetries of the S--matrix. We discuss the…

High Energy Physics - Theory · Physics 2014-08-19 Paul Dempster , Mirian Tsulaia

In this article we prove that for a large class of 2-dimensional minimal cones (including almost all 2-dimensional minimal cones that we know), the almost orthogonal union of any two of them is still a minimal cone. Comparing to existing…

Classical Analysis and ODEs · Mathematics 2018-08-30 Xiangyu Liang

Given a five dimensional space endowed with a Cartan distribution, the abnormal geodesics form another five dimensional space with a cone structure. Then it is shown, if the cone structure is regarded as a control system, then, the space of…

Differential Geometry · Mathematics 2014-03-25 G. Ishikawa , Y. Kitagawa , W. Yukuno

We give a soft geometric proof of the classical result due to Conn stating that a Poisson structure is linearizable around a singular point (zero) at which the isotropy Lie algebra is compact and semisimple.

Symplectic Geometry · Mathematics 2008-12-17 Marius Crainic , Rui Loja Fernandes

In this paper the concept of a partial cone metric space is investigated, some continuity type theorems, and fixed point theorems of contractive mappings in this generalized setting are proved as well as some theorems related to topological…

General Topology · Mathematics 2012-09-20 Ayse Sonmez

We show that directed minimal cones in (n+1)-dimensional Euclidean space which have at most one singularity are - besides the trivial cases: empty set, whole space - half spaces. Using blow-up techniques, this result can be used to get…

Analysis of PDEs · Mathematics 2007-05-23 Oliver C. Schnuerer

At very low density, the electrons in a uniform electron gas spontaneously break symmetry and form a crystalline lattice called a Wigner crystal. But which type of crystal will the electrons form? We report a numerical study of the density…

Let $X$ be a quasi-projective curve, compactified to $(Y,D)$ with $X=Y-D$. We construct a Deligne-Hitchin twistor space out of moduli spaces of framed $\lambda$-connections of rank $2$ over $Y$ with logarithmic singularities and…

Algebraic Geometry · Mathematics 2021-11-02 Carlos Simpson

Partial cubes are isometric subgraphs of hypercubes. Structures on a graph defined by means of semicubes, and Djokovi\'{c}'s and Winkler's relations play an important role in the theory of partial cubes. These structures are employed in the…

Combinatorics · Mathematics 2007-05-23 Sergei Ovchinnikov

The paper focuses on the conformal Lorentz geometry of quasi-umbilical timelike surfaces in the $(1+2)$-Einstein universe, the conformal compactification of Minkowski 3-space realized as the space of oriented null lines through the origin…

Differential Geometry · Mathematics 2025-09-29 Emilio Musso , Lorenzo Nicolodi , Mason Pember

We study surfaces in Euclidean space constructed by the sum of two curves or that are graphs of the product of two functions. We consider the problem to determine all these surfaces with constant Gauss curvature. We extend the results to…

Differential Geometry · Mathematics 2014-10-10 Rafael López , Marilena Moruz

We investigate the stability of the Wasserstein distance, a metric structure on the space of probability measures arising from the theory of optimal transport, under metric ultralimits. We first show that if $(X_{i},d_{i})_{i\in\mathbb{N}}$…

Metric Geometry · Mathematics 2023-03-09 Andrew Warren

General definitions for causal structures on manifolds of dimension d+1>2 are presented for the topological category and for any differentiable one. Locally, these are given as cone structures via local (pointwise) homeomorphic or…

General Relativity and Quantum Cosmology · Physics 2015-06-25 Martin Rainer

We introduce Lorentz spaces $L_{p(\cdot),q}(\R^n)$ and $L_{p(\cdot),q(\cdot)}(\R^n)$ with variable exponents. We prove several basic properties of these spaces including embeddings and the identity…

Functional Analysis · Mathematics 2013-08-27 Henning Kempka , Jan Vybíral

The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the image of a non-closed geodesic has 0 distance from the set of conical points.…

Geometric Topology · Mathematics 2016-03-08 Charalampos Charitos , Ioannis Papadoperakis , Georgios Tsapogas

We study some structural aspects of the subspaces of the non-commutative (Haagerup) L_p-spaces associated with a general (non necessarily semi-finite) von Neumann algebra A. If a subspace X of L_p(A) contains uniformly the spaces \ell_p^n,…

Functional Analysis · Mathematics 2019-12-10 Yves Raynaud , Quanhua Xu

The embedding of a given point set with non-crystallographic symmetry into higher-dimensional space is reviewed, with special emphasis on the Minkowski embedding known from number theory. This is a natural choice that does not require an a…

Materials Science · Physics 2016-10-06 Michael Baake , David Ecija , Uwe Grimm

We study the reflectional symmetry of a surface in the Euclidean 3-dimensional space with a cross-cap singularity with respect to planes. This symmetry is picked up by the singularities of folding maps on the cross-cap. We give a list of…

Differential Geometry · Mathematics 2020-04-13 Martín Barajas Sichacá

We compare the structure of a mapping cone in the category Top^D of spaces under a space D with differentials in algebraic models like crossed complexes and quadratic complexes. Several subcategories of Top^D are identified with algebraic…

Algebraic Topology · Mathematics 2010-05-27 Hans-Joachim Baues , Beatrice Bleile