On the Dirichlet Problem at Infinity for Manifolds of Nonpositive Curvature.
On the distribution of resonances for some asymptotically hyperbolic manifolds
We establish a sharp upper bound for the resonance counting function for a class of asymptotically hyperbolic manifolds in arbitrary dimension, including convex, cocompact hyperbolic manifolds in two dimensions. The proof is based on the construction of a suitable paramatrix for the absolute -matrix that is unitary for real values of the energy. This paramatrix is the -matrix for a model laplacian corresponding to a separable metric near infinity. The proof of the upper bound on the resonance...
On the error term in Weyl's law for Heisenberg manifolds
On the eta invariant, stable positive scalar curvature, and Higher -genera.
On the existence of nodal solutions for a nonlinear elliptic problem on symmetric Riemannian manifolds.
On the Fefferman-Phong inequality
We show that the number of derivatives of a non negative 2-order symbol needed to establish the classical Fefferman-Phong inequality is bounded by improving thus the bound obtained recently by N. Lerner and Y. Morimoto. In the case of symbols of type , we show that this number is bounded by ; more precisely, for a non negative symbol , the Fefferman-Phong inequality holds if are bounded for, roughly, . To obtain such results and others, we first prove an abstract result which says that...
On the first eigenvalue of the Laplacian for compact submanifolds of Euclidean space.
On the fixed point formula for Atiyah and Bott
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 Heat Equation and the Index Theorem.
On the Independence of Exit Time and Exit Position from Small Geodesic Balls for Brownian Motions on Riemannian Manifolds.
On the Index of Callias-type Operators.
On the index of nonlocal elliptic operators for compact Lie groups
We consider a class of nonlocal operators associated with a compact Lie group G acting on a smooth manifold. A notion of symbol of such operators is introduced and an index formula for elliptic elements is obtained. The symbol in this situation is an element of a noncommutative algebra (crossed product by G) and to obtain an index formula, we define the Chern character for this algebra in the framework of noncommutative geometry.
On the index theorem for symplectic orbifolds
We give an explicit construction of the trace on the algebra of quantum observables on a symplectiv orbifold and propose an index formula.
On the Initial-Boundary Value Problem for Harmonic Maps from the 2-Dimensional Minkowski Space.
On the integrability of a -conformal Killing equation in a Kaehlerian manifold.
On the intersection forms of spin 4-manifolds bounded by spherical 3-manifolds.
On the inversion of pseudo-differential operators
On the index of spin Dirac operators on conical manifolds
We compute the index of the Dirac operator on a spin Riemannian manifold with conical singularities, acting from to with p,q > 1. When 1 + n/p - n/q > 0 we obtain the usual Atiyah-Patodi-Singer formula, but with a spectral cut at (n+1)/2 - n/q instead of 0 in the definition of the eta invariant. In particular we reprove Chou’s formula for the L² index. For 1 + n/p - n/q ≤ 0 the index formula contains an extra term related to the Calderón projector.