A characterization for isometries and conformal mappings of pseudo-Riemannian manifolds.
A generalization of Nehari's univalence criterion.
A Monge-Ampère equation in conformal geometry
We consider the Monge-Ampère-type equation , where is the Schouten tensor of a conformally related metric and is a suitably chosen constant. When the scalar curvature is non-positive we give necessary and sufficient conditions for the existence of solutions. When the scalar curvature is positive and the first Betti number of the manifold is non-zero we also establish existence. Moreover, by adapting a construction of Schoen, we show that solutions are in general not unique.
A New Conformal Invariant and Its Applications to the Wilmore Conjecture and the First Eigenvalue of Compact Surfaces.
A note on conformal vector fields on a Riemannian manifold
We consider an n-dimensional compact Riemannian manifold (M,g) and show that the presence of a non-Killing conformal vector field ξ on M that is also an eigenvector of the Laplacian operator acting on smooth vector fields with eigenvalue λ > 0, together with an upper bound on the energy of the vector field ξ, implies that M is isometric to the n-sphere Sⁿ(λ). We also introduce the notion of φ-analytic conformal vector fields, study their properties, and obtain a characterization of n-spheres...
A Note on Curvature-like Invariants of Some Connections on Locally Decomposable Spaces
A note on surfaces with prescribed oriented Euclidean Gauss map.
A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds (Summary).
A Singularity Theorem for Twistor Spinors
We study spin structures on orbifolds. In particular, we show that if the singular set has codimension greater than 2, an orbifold is spin if and only if its smooth part is. On compact orbifolds, we show that any non-trivial twistor spinor admits at most one zero which is singular unless the orbifold is conformally equivalent to a round sphere. We show the sharpness of our results through examples.
A strong maximum principle for the Paneitz operator and a non-local flow for the -curvature
In this paper we consider Riemannian manifolds of dimension , with semi-positive -curvature and non-negative scalar curvature. Under these assumptions we prove (i) the Paneitz operator satisfies a strong maximum principle; (ii) the Paneitz operator is a positive operator; and (iii) its Green’s function is strictly positive. We then introduce a non-local flow whose stationary points are metrics of constant positive -curvature. Modifying the test function construction of Esposito-Robert, we show...
Algèbres de Clifford dégénérées et revêtements des groupes conformes affines orthogonaux et symplectiques
An integral equation in conformal geometry
An ODE approach to the equation ... U + Ku ... = 0, in Rn.
Application of spaces of subspheres to conformal invariants of curves and canal surfaces
We review some techniques from the Möbius geometry of curves and surfaces in the 3-sphere, consider canal surfaces using their characteristic circles, and express the conformal curvature, and conformal torsion, of a vertex-free space curve in terms of its corresponding curve of osculating circles, and osculating spheres, respectively. We accomplish all of this strictly within the framework of Möbius geometry, and compare our results with the literature. Finally, we show how our formulation allows...