Related papers: Structures conformes asymptotiquement plates
We review the structure of W_\infty algebras, their super and topological extensions, and their contractions down to (super) w_\infty. Emphasis is put on the field theoretic realisations of these algebras. We also review the structure of…
This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.
We present a geometric construction and characterization of $2n$-dimensional split-signature conformal structures endowed with a twistor spinor with integrable kernel. The construction is regarded as a modification of the conformal…
We give an explicit description of "bundles of conformal blocks" in Wess-Zumino-Witten models of Conformal field theory and prove that integral representations of Knizhnik-Zamolodchikov equations constructed earlier by the second and third…
We present a classification theorem for closed smooth spin 2-connected 7-manifolds M. This builds on the almost-smooth classification from the first author's thesis. The main additional ingredient is an extension of the Eells-Kuiper…
We discuss solutions of several questions concerning the geometry of conformal planes.
An enhanced version of the conformal BMS$_{3}$ algebra is presented. It is shown to emerge from the asymptotic structure of an extension of conformal gravity in 3D by Pope and Townsend that consistently accommodates an additional spin-2…
We propose two new conformity scores for conformal prediction, in a general multivariate regression framework. The underlying score functions are based on a covariance analysis of the residuals and the input points. We give theoretical…
Comparison theorems are foundational to our understanding of the geometric features implied by various curvature constraints. This paper considers manifolds with a positive lower bound on either scalar, 2-Ricci, or Ricci curvature, and…
We classify spin structures on the noncommutative torus, and find that the noncommutative n-torus has 2^n spin structures, corresponding to isospectral deformations of spin structures on the commutative n-torus. For n>3 the classification…
In this paper, we investigate the weighted mass for weighted manifolds. By establishing a version of density theorem and generalizing Geroch conjecture in the setting of $P$-scalar curvature, we are able to prove the positive weighted mass…
Conformal invariance plays a significant role in many areas of Physics, such as conformal field theory, renormalization theory, turbulence, general relativity. Naturally, it also plays an important role in geometry: theory of Riemannian…
We study the Jones and Tod correspondence between selfdual conformal 4-manifolds with a conformal vector field and abelian monopoles on Einstein-Weyl 3-manifolds, and prove that invariant complex structures correspond to shear-free geodesic…
We classify ${\cal N}=1$ gauge theories with simple gauge groups in four dimensions which possess a conformal manifold passing through weak coupling. A very rich variety of models is found once one allows for arbitrary representations under…
This is the second in a two part series of papers concerning Morse quasiflats - higher dimensional analogs of Morse quasigeodesics. Our focus here is on their asymptotic structure. In metric spaces with convex geodesic bicombings, we prove…
This is an invited contribution to the 2nd edition of the Encyclopedia of Mathematical Physics. We review the following algebraic structures which appear in two-dimensional conformal field theory (CFT): The symmetries of two-dimensional…
We describe the different classes of $\mathrm{Spin(7)}$ structures in terms of spinorial equations. We relate them to the spinorial description of $\mathrm{G}_2$ structures in some geometrical situations. Our approach enables us to analyze…
We give some rigidity theorems for an n$(\geq4)$-dimensional compact Riemannian manifold with harmonic Weyl curvature, positive scalar curvature and positive constant $\sigma_2$. Moreover, when $n=4,$ we prove that a 4-dimensional compact…
This paper presents two existence h-principles, the first for conformal symplectic structures on closed manifolds, and the second for leafwise conformal symplectic structures on foliated manifolds with non empty boundary. The latter…
We examine the variational and conformal structures of higher order theories of gravity which are derived from a metric-connection Lagrangian that is an arbitrary function of the curvature invariants. We show that the constrained first…