Gilles Carron

Eigenvalues and holonomy

We estimate the eigenvalues of connection Laplacians in terms of the non-triviality of the holonomy.

Conformally flat manifolds with nonnegative Ricci curvature

We show that complete conformally flat manifolds of dimension n>2 with nonnegative Ricci curvature enjoy nice rigidity properties: they are either flat, or locally isometric to a product of a sphere and a line, or are globally conformally equivalent to flat space or to a spherical spaceform. This extends previous works by Q.-M. Cheng, M.H. Noronha, B.-L. Chen and X.-P. Zhu, and S. Zhu.

On the quasi-asymptotically locally Euclidean geometry of Nakajima's metric

We show that on Hilbert scheme of

A Topological Criterion for the Existence of Half-Bound States

n

Index theorems on manifolds with straight ends

points on

Erratum to "The Huber theorem for non-compact conformally flat manifolds"

\C^2

The Huber theorem for non-compact conformally flat manifolds

, the hyperkahler metric construsted by H. Nakajima via hyperkahler reduction is the Quasi-Asymptotically Locally Euclidean (QALE in short) metric constructed by D. Joyce.

The Yamabe problem on stratified spaces

The following theorem is proved: if (M 4n+1 ;g) is a complete Riemannian manifold and M is an oriented hypersurface partitioning M and with non-zero signature, then the spectrum of the Hodge{ deRham Laplacian is [0;1[. This result is obtained by a new Callias-type index. This new formula links half-bound harmonic forms (that is, nearly L 2 but not in L 2 ) with the signature of .

Regularity and index theory for Dirac-Schrödinger systems with Lipschitz coefficients

We study Fredholm properties and index formulas for Dirac operators over complete Riemannian manifolds with straight ends. An important class of examples of such manifolds are complete Riemannian manifolds with pinched negative sectional curvature and finite volume.

Le saut en zéro de la fonction de décalage spectral

An argument in our paper The Huber theorem for non-compact conformally flat manifolds [Comment. Math. Helv. 77 (2002), 192?220] was not justified. Using recent work by G. Tian and J. Viaclovsky, we show that our result holds true