Analysis on Kähler and Lorentzian manifolds

by Nicolas Ginoux

Habilitation thesis, Universität Regensburg

Defended on November 7, 2013 - Certificate handed on May 14, 2014

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Abstract: This habilitation thesis deals with the interactions between geometry of and analysis on smooth manifolds in different situations. Chapter 1 summarises all the results obtained in the next chapters. Chapter 2 deals with the spectrum of the Dirac operator of the Berger metrics on a 3-dimensional space. Estimates on the smallest eigenvalues of twisted Dirac operators on the complex projective space are computed and their limiting-case discussed in chapter 3. Chapter 4 focuses on a purely geometric question of classifying those Kähler spin manifolds with imaginary Kählerian Killing spinors. In chapter 5, we address the Yamabe problem on globally hyperbolic spacetimes. Chapter 6 is concerned with locally covariant quantization of fields for a large class of differential operators on spacetimes.

Nicolas Ginoux, 21.05.2014