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Special submanifolds of Spin$^c$ manifolds
In this thesis, we aim to make use of Spin$^c$ geometry to study special submanifolds. We start by establishing basic results for the Spin$^c$ Dirac operator. We give... -
A nonlinear variational problem in relativistic quantum mechanics
Proceeding from the 6th European Congress of Mathematics at Krakow (Poland), July 2012 -
INDEX THEOREMS ON MANIFOLDS WITH STRAIGHT ENDS.
International audience -
A variational study of some hadron bag models
Quantum chromodynamics (QCD) is the theory of strong interaction and accounts for the internal structure of hadrons. Physicists introduced phe- nomenological models... -
Surgery and Harmonic Spinors
Let M be a compact manifold with a fixed spin structure \chi. The Atiyah-Singer index theorem implies that for any metric g on M the dimension of the kernel of the... -
Spinorial representation of surfaces in four-dimensional Space Forms
International audience -
Exponential Estimate for the asymptotics of Bergman kernels
correct version, 15 pages -
Theoretical and numerical study of nonlinear models in quantum mechanics
This thesis is concerned with several mathematical problems in quantum mechanics. These problems arise naturally in quantum chemistry in connection with the electronic... -
Variational and topological methods for the study of nonlinear models from re...
This thesis is devoted to the study of nonlinear models from relativistic quantum mechanics.In the first part, we show thanks to a shooting method, the existence of... -
A Pohozaev type identity for Dirac operators
International audience -
Manifolds with small Dirac eigenvalues are nilmanifolds
a paraitre dans Annals of Global Analysis and Geometry -
Spinors and isometric immersions of surfaces in 4-dimensional products
International audience -
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... -
Semi-classical properties of Berezin--Toeplitz operators with $\cC^k$--\,symbol
Final version, 27 pages
