arXiv research

Analyzes conformal anomaly in five dimensions, identifying new boundary conformal invariants.

Variationality of conformal geodesics fails in higher dimensions.

The study finds limits on dimensions of certain scales and fields for conformal manifolds.

Study proves higher-order conformal forms don't exist in odd dimensions.

The paper applies potential theory to conformal geometry, proving theorems and dimension estimates.

Enhances conformal geometry in higher dimensions with infinite-dimensional algebra.

The study explores conformal symplectic foliations on closed manifolds, proving their existence in dimensions 5 and above.

We show that C^2 conformally compact Riemannian Einstein metrics have conformal compactifications that are smooth up to the boundary in dimension 3 and all even dimensions, and polyhomogeneous in odd dimensions greater than 3.

In low dimensions, minimizers for the second conformal eigenvalue do not exist near the round sphere.

In 3D, conformal geodesics are variational.

In this note we prove that a generic Riemannian manifold of dimension $\geq 3$ does not admit any nontrivial local conformal diffeomorphisms. This is a conformal analog of a result of Sunada concerning local isometries, and makes precise the principle that generic manifolds in high dimensions do not have conformal symm…

Local supertwistors help study 6D conformal supergravity.

Upper bounds for volume spectrum depend on volume, dimension, and a conformal invariant.

We classify the harmonic morphisms with one-dimensional fibres (1) from real-analytic conformally-flat Riemannian manifolds of dimension at least four, and (2) between conformally-flat Riemannian manifolds of dimensions at least three.

New algebraic approach classifies conformally superintegrable systems in arbitrary dimensions.

We find new bounds on the conformal dimension of small cancellation groups. These are used to show that a random few relator group has conformal dimension 2+o(1) asymptotically almost surely (a.a.s.). In fact, if the number of relators grows like l^K in the length l of the relators, then a.a.s. such a random group has …

We produce some explicit examples of conformally compact Einstein manifolds, whose conformal compactifications are foliated by Riemannian products of a closed Einstein manifold with the total space of a principal circle bundle over products of Kahler-Einstein manifolds. We compute the associated conformal invariants, i…

This paper presents conformal invariants for Riemannian manifolds of dimension greater than or equal to four whose vanishing is necessary for a Riemannian manifold to be conformally related to an Einstein space. One of the invariants is a modification of the Cotton tensor, the other is a $n$--dimensional version of the…

Study finds a linear lower bound on conformal dimension for random hyperbolic groups.

Superintegrable systems on surfaces are classified geometrically.

Study of conformally compact metrics and Lovelock tensors in even dimensions.

Researchers found spiraling conformal geodesics in 3D space.

We characterize manifolds which are locally conformally equivalent to either complex projective space or to its negative curvature dual in terms of their Weyl curvature tensor. As a byproduct of this investigation, we classify the conformally complex space forms if the dimension is at least 8. We also study when the Ja…

Let (M,g) be a compact Riemannian manifold of dimension >2. We show that there is a metric h conformal to g and of volume 1 such that the first positive eigenvalue the conformal Laplacian with repect to h is arbitrarily large. A similar statement is proven for the first positive eigenvalue of the Dirac operator on a sp…

Bounds on conformal dimension for certain Coxeter group boundaries.

Let (M,g) be an arbitrary pseudo-Riemannian manifold of dimension at least 3. We determine the form of all the conformal symmetries of the conformal (or Yamabe) Laplacian on (M,g), which are given by differential operators of second order. They are constructed from conformal Killing 2-tensors satisfying a natural and c…

We give global restrictions on the possible boundaries of compact, orientable, locally conformally flat manifolds of dimension $4k$ in terms of integrality of eta invariants.

Sharp characterization of Willmore invariant in higher dimensions.

We show that in dimension n>3 the class of simple conformally recurrent space-times coincides with the class of conformally recurrent pp-waves.

The Fefferman metric connects CR manifolds to conformal geodesics in 3D.

We derive some necessary conditions on a Riemannian metric $(M, g)$ in four dimensions for it to be locally conformal to Kähler. If the conformal curvature is non anti--self--dual, the self--dual Weyl spinor must be of algebraic type $D$ and satisfy a simple first order conformally invariant condition which is necessar…

We obtain an Einstein metric of constant negative curvature given an arbitrary boundary metric in three dimensions, and a conformally flat one given an arbitrary conformally flat boundary metric in other dimensions. In order to compute the on-shell value of the gravitational action for these solutions, we propose to in…

We establish the existence of solvable Lie groups of dimension 4 and left-invariant Riemannian metrics with zero Bach tensor which are neither conformally Einstein nor half conformally flat.

Explicit models for the restricted conformal group of the Einstein static universe of dimension greater than two and for its universal covering group are constructed. Based on these models, as an application we determine all oriented and time-oriented conformal Lorentz manifolds whose restricted conformal group has max…

Study on filling 3D metrics with 4D Poincaré-Einstein structures.

In this paper we provide a criteria for geometric finiteness of Kleinian groups in general dimension. We formulate the concept of conformal finiteness for Kleinian groups in space of dimension higher than two, which generalizes the notion of analytic finiteness in dimension two. Then we extend the argument in the paper…

Study shows strict inequality for Dirac-type equation on spin manifolds, leading to existence results.

Rado's theorem shows all conformal manifolds are paracompact.

The study examines non-Kähler threefolds with specific metrics and finds they are quasi-bundles over surfaces.

Efficiently samples conformal boundaries in high dimensions using flows.

On a conformal manifold, it is well known that parallel sections of the standard tractor bundle with non-vanishing scale are in 1-1 correspondence with solutions of the conformal Einstein equation. In 2 dimensions conformal geometry carries no local information but one can remedy this by equipping the surface with a Mö…

We study the renormalized volume of a conformally compact Einstein manifold. In even dimensions, we derive the analogue of the Chern-Gauss-Bonnet formula incorporating the renormalized volume. When the dimension is odd, we relate the renormalized volume to the conformal primitive of the $Q$-curvature. We show how all t…

Conformer encoder reverses sequence in time dimension, affecting decoder training.

Characterizes conformal classes of tori using differential geometry.

In this paper we prove that every Riemannian metric on a locally conformally flat manifold with umbilic boundary can be conformally deformed to a scalar flat metric having constant mean curvature. This result can be seen as a generalization to higher dimensions of the well known Riemann mapping Theorem in the plane.

The paper derives estimates for linear potentials and applies them to improve Hausdorff dimensions of singular sets in conformal geometry.

Inspired by the all-important conformal invariance of harmonic maps on two-dimensional domains, this article studies the relationship between biharmonicity and conformality. We first give a characterization of biharmonic morphisms, analogues of harmonic morphisms investigated by Fuglede and Ishihara, which, in particul…

3D projective structures can be metrized with conformal structures.