The main idea behind noncommutative geometry (see [Connes (1994)] for an extensive
treatment of the subject) lies in the correspondence between spaces and algebras of …

Let M be a compact manifold equipped with a Riemannian metric g and a spin structure\si.
We let $\lambda (M,[g],\si)=\inf_ {\tilde {g}\in [g]}\lambda_1^+(\tilde {g}) Vol (M,\tilde {g})^{1/n} …

The spectral action functional, considered as a model of gravity coupled to matter, provides,
in its non-perturbative form, a slow-roll potential for inflation, whose form and corresponding …

In this paper we study the problem of prescribing Dirichlet eigenvalues on an arbitrary
compact manifold M of dimension n≥ 3 with a non-empty smooth boundary∂ M. We show …

In the present paper, we consider Dirichlet Laplacian on compact surface. We show that for
a fixed surface with boundary X, a finite increasing sequence of real numbers 0< a 1< a …

Abstract Let (M, g, σ) be a compact Riemannian spin manifold of dimension m≥ 2, let S (M)
denote the spinor bundle on M, and let D be the Atiyah-Singer Dirac operator acting on …

Sur toute variété compacte de dimension n≥ 3 à bord, on prescrit toute partie finie du
spectre de Steklov dans une classe conforme donnée. En particulier, on prescrit la …

Sur toute variété compacte de dimension supérieure ou égale à 6, on prescrit le volume et le
début du spectre du laplacien de Hodge–de Rham agissant sur les p-formes différentielles …

On any compact manifold of dimension greater than 4, we prescribe the volume and any
finite part of the spectrum of the Witten Laplacian acting on $ p $-form for $0< p< n $. In …

Let M be a closed spin manifold of dimension at least three with a fixed topological spin
structure. For any Riemannian metric, we can construct the associated Dirac operator. The …