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Complex Hessian equations on some compact Kähler manifolds
On a compact connected $2m$-dimensional Kähler manifold with Kähler form $ \omega $, given a volume form $\Omega \in [\omega ]^m$ and an integer $1 -
Upper bounds for eigenvalues of natural operators on compact Riemannian manif...
The purpose of this thesis is to find upper bounds for the eigenvalues of natural operators acting on functions on a compact Riemannian manifold $(M,g)$ such as the... -
Commutator, spectral analysis and application
We present the theory of positive commutator and its recent improvements. We discuss applications to the spectral analysis of magnetic Laplacians on manifolds,... -
Spectral approximation with matrices issued from discretized operators
In this thesis, we consider the numerical solution of a large eigenvalue problem in which the integral operator comes from a radiative transfer problem. It is... -
Conformal aspect of the Dirac operator on manifolds with boundary
In this thesis, we study the conformal aspect of the spectrum of the Dirac operator on manifolds with boundary. First, we prove some lower bounds for the first...
