Related papers: The Moyal Sphere
We consider the problem of finding a metric in a given conformal class with prescribed nonpositive scalar curvature and nonpositive boundary mean curvature on a compact manifold with boundary, and establish a necessary and sufficient…
We discuss notions of Gauss curvature and mean curvature for polyhedral surfaces. The discretizations are guided by the principle of preserving integral relations for curvatures, like the Gauss/Bonnet theorem and the mean-curvature force…
In this paper we introduce a class of polygonal complexes for which we can define a notion of sectional combinatorial curvature. These complexes can be viewed as generalizations of 2-dimensional Euclidean and hyperbolic buildings. We focus…
In this paper, we consider the following curvature equation $$\Delta u+{\rm e}^u=4\pi\biggl((\theta_0-1)\delta_0+(\theta_1-1)\delta_1 +\sum_{j=1}^{n+m}\bigl(\theta_j'-1\bigr)\delta_{t_j}\biggr)\qquad \text{in}\ \mathbb R^2,$$…
We use results from time-frequency analysis and Gabor analysis to construct new classes of sigma-model solitons over the Moyal plane and over noncommutative tori, taken as source spaces, with a target space made of two points. A natural…
We build a differential calculus for subalgebras of the Moyal algebra on R^4 starting from a redundant differential calculus on the Moyal algebra, which is suitable for reduction. In some cases we find a frame of 1-forms which allows to…
We consider the problem of finding a metric in a given conformal class with prescribed non-positive scalar curvature and non-positive boundary mean curvature on an asymptotically Euclidean manifold with inner boundary. We obtain a necessary…
To study asymptotic structures, we regularize Einstein's field equations by means of conformal transformations. The conformal factor is chosen so that it carries a dimensional scale that captures crucial asymptotic features. By choosing a…
Natural metric structures on tangent bundles and tangent sphere bundles enclose many important problems, from the topology of the base to the determination of their holonomy. We make here a brief study of the topic. We find the…
A discrete conformality for hyperbolic polyhedral surfaces is introduced in this paper. This discrete conformality is shown to be computable. It is proved that each hyperbolic polyhedral metric on a closed surface is discrete conformal to a…
A new 8-dim conformal gauging solves the auxiliary field problem and eliminates unphysical size change from Weyl's electromagnetic theory. We derive the Maurer-Cartan structure equations and find the zero curvature solutions for the…
We introduce a family of conformal invariants associated to a smooth metric measure space which generalize the relationship between the Yamabe constant and the best constant for the Sobolev inequality to the best constants for…
We analyze a novel approach to gauging rigid higher derivative (higher spin) symmetries of free relativistic actions defined on flat spacetime, building on the formalism originally developed by Bonora et al. and Bekaert et al. in their…
We develop a transitional geometry, that is, a family of geometries of constant curvatures which makes a continuous connec-tion between the hyperbolic, Euclidean and spherical geometries. In this transitional setting, several geometric…
Let $(M, g)$ be a compact Riemannian manifold with boundary $\partial M$. Given a function $f$ on $\partial M$, we consider the problem of finding a conformal metric of $g$ with zero scalar curvature in $M$ and prescribed mean curvature $f$…
We establish several nonuniqueness results for the problem of finding complete conformal metrics with constant (fourth-order) $Q$-curvature on compact and noncompact manifolds of dimension $\geq5$. Infinitely many branches of metrics with…
We construct universal geometric coefficients for the cluster algebra associated to the four-punctured sphere and obtain, as a by-product, the g-vectors of cluster variables. We also construct the rational part of the mutation fan. These…
We consider axially symmetric static metrics in arbitrary dimension, both with and without a cosmological constant. The most obvious such solutions have an SO(n) group of Killing vectors representing the axial symmetry, although one can…
The Maxwell extension of the conformal algebra is presented. With the help of gauging the Maxwell-conformal group, a conformally invariant theory of gravity is constructed. In contrast to the conventional conformally invariant actions, our…
For matrix analogues of embedded surfaces we define discrete curvatures and Euler characteristics, and a non-commutative Gauss--Bonnet theorem is shown to follow. We derive simple expressions for the discrete Gauss curvature in terms of…