Juan Pablo Navarrete – författare

This proceedings volume gathers selected, revised papers presented at the XI International Meeting on Lorentzian Geometry (GeLoMer 2024), held at the Autonomous University of Yucatán, Mexico, from January 29 to February 2, 2024.Lorentzian geometry provides the mathematical foundation for Einstein's theory of relativity. It incorporates aspects from different branches of mathematics, such as differential geometry, partial differential equations, and mathematical analysis, to name a few.This volume includes surveys describing the state-of-the-art in specific areas, and a selection of the most relevant results presented at the conference, which is seen as a benchmark for those working in Lorentz geometry due to its relevance.Given its scope, the book will be of interest to both young and experienced mathematicians and physicists whose research involves general relativity and semi-Riemannian geometry.

This proceedings volume gathers selected, revised papers presented at the XI International Meeting on Lorentzian Geometry (GeLoMer 2024), held at the Autonomous University of Yucatán, Mexico, from January 29 to February 2, 2024.Lorentzian geometry provides the mathematical foundation for Einstein's theory of relativity. It incorporates aspects from different branches of mathematics, such as differential geometry, partial differential equations, and mathematical analysis, to name a few.This volume includes surveys describing the state-of-the-art in specific areas, and a selection of the most relevant results presented at the conference, which is seen as a benchmark for those working in Lorentz geometry due to its relevance.Given its scope, the book will be of interest to both young and experienced mathematicians and physicists whose research involves general relativity and semi-Riemannian geometry.

This monograph lays down the foundations of the theory of complex Kleinian groups, a newly born area of mathematics whose origin traces back to the work of Riemann, Poincaré, Picard and many others. Kleinian groups are, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can be regarded too as being groups of holomorphic automorphisms of the complex projective line CP1. When going into higher dimensions, there is a dichotomy: Should we look at conformal automorphisms of the n-sphere?, or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories are different in higher dimensions. In the first case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition. In the second case we are talking about an area of mathematics that still is in its childhood, and this is the focus of study in this monograph. This brings together several important areas of mathematics, as for instance classical Kleinian group actions, complex hyperbolic geometry, chrystallographic groups and the uniformization problem for complex manifolds.​

This monograph lays down the foundations of the theory of complex Kleinian groups, a newly born area of mathematics whose origin traces back to the work of Riemann, Poincaré, Picard and many others. Kleinian groups are, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can be regarded too as being groups of holomorphic automorphisms of the complex projective line CP1. When going into higher dimensions, there is a dichotomy: Should we look at conformal automorphisms of the n-sphere?, or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories are different in higher dimensions. In the first case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition. In the second case we are talking about an area of mathematics that still is in its childhood, and this is the focus of study in this monograph. This brings together several important areas of mathematics, as for instance classical Kleinian group actions, complex hyperbolic geometry, chrystallographic groups and the uniformization problem for complex manifolds.​