On the eta invariant, stable positive scalar curvature, and Higher -genera.
On the Example of Almost Pseudo-Z-symmetric Manifolds
In the present paper we have obtained a new example of non-Ricci-flat almost pseudo-Z-symmetric manifolds in the class of equidistant spaces, which admit non-trivial geodesic mappings.
On the existence of positive solutions of semilinear elliptic equations with Dirichlet boundary conditions.
On the finiteness of the fundamental group of a compact shrinking Ricci soliton
Myers's classical theorem says that a compact Riemannian manifold with positive Ricci curvature has finite fundamental group. Using Ambrose's compactness criterion or J. Lott's results, M. Fernández-López and E. García-Río showed that the finiteness of the fundamental group remains valid for a compact shrinking Ricci soliton. We give a self-contained proof of this fact by estimating the lengths of shortest geodesic loops in each homotopy class.
On the four-dimensional -manifolds of positive Ricci curvature.
On the generic spectrum of a riemannian cover
Let be a compact manifold let be a finite group acting freely on , and let be the (Fréchet) space of -invariant metric on . A natural conjecture is that, for a generic metric in , all eigenspaces of the Laplacian are irreducible (as orthogonal representations of ). In physics terminology, no “accidental degeneracies” occur generically. We will prove this conjecture when dim dim for all irreducibles of . As an application, we construct isospectral manifolds with simple eigenvalue...
On the geometry of Riemannian manifolds with a Lie structure at infinity.
On the multiplicity of eigenvalues of conformally covariant operators
Let be a compact Riemannian manifold and an elliptic, formally self-adjoint, conformally covariant operator of order acting on smooth sections of a bundle over . We prove that if has no rigid eigenspaces (see Definition 2.2), the set of functions for which has only simple non-zero eigenvalues is a residual set in . As a consequence we prove that if has no rigid eigenspaces for a dense set of metrics, then all non-zero eigenvalues are simple for a residual set of metrics in the -topology....
On the non-existence of certain ovaloids
On the Paneitz energy on standard three sphere
We prove that the Paneitz energy on the standard three-sphere is bounded from below and extremal metrics must be conformally equivalent to the standard metric.
On the Paneitz energy on standard three sphere
We prove that the Paneitz energy on the standard three-sphere S3 is bounded from below and extremal metrics must be conformally equivalent to the standard metric.
On the uniqueness of solutions of the homogeneous curvature equations
Opérateurs géométriques et géométrie conforme