The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs.
The bottom of the spectrum of a Riemannian covering.
The determinant of the Laplacian on the n-sphere
The Differential Form Spectrum of Hyperbolic Space.
The Dirac operator on collapsing -bundles
The distribution of eigenvalues of partial differential operators
The eigenvalues of the Laplacian for the homology of the Lie algebra corresponding to a poset.
The eta invariant and metrics of positive scalar curvature.
The first eigenvalue of a Riemann surface.
The first eigenvalue of spacelike submanifolds in indefinite space form
In this paper, we prove that the first eigenvalue of a complete spacelike submanifold in with the bounded Gauss map must be zero.
The first eigenvalue of the laplacian for a positively curved homogeneous riemannian manifold
The free laplacian with attractive boundary conditions
The fundamental group and the spectrum of the Laplacian.
The gaps in the spectrum of the Schrödinger operator
We obtain inequalities between the eigenvalues of the Schrödinger operator on a compact domain Ω of a submanifold M in with boundary ∂Ω, which generalize many existing inequalities for the Laplacian on a bounded domain of a Euclidean space. We also establish similar inequalities for a closed minimal submanifold in the unit sphere, which generalize and improve Yang-Yau’s result.
The geometry and spectrum of the one holed torus.
The heat semigroup acting on tensors or differential forms with values in vector bundle
The Hijazi inequalities on complete Riemannian manifolds.
The Hodge laplacian on manifolds with boundary
The inaudible geometry of nilmanifolds.
The Laplace operator on a hyperbolic manifold. II. Eisenstein series and the scattering matrix.