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Hyperbolic geometry

Jacques Franchi and Yves Le Jan

in Hyperbolic Dynamics and Brownian Motion: An Introduction

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199654109
eISBN:
9780191745676
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199654109.003.0002
Subject:
Mathematics, Mathematical Physics

Basic notions of hyperbolic geometry are presented: geodesics, light rays, tangent bundles etc. These are systematically derived from properties of Minkowski space: the boundary of hyperbolic space ... More


Hyperbolic Dynamics and Brownian Motion: An Introduction

Jacques Franchi and Yves Le Jan

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199654109
eISBN:
9780191745676
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199654109.001.0001
Subject:
Mathematics, Mathematical Physics

The idea of this book is to illustrate an interplay between distinct domains of mathematics. Firstly, this book provides an introduction to hyperbolic geometry, based on the Lorentz group PSO(1, d) ... More


Hypoelliptic Laplacian and Orbital Integrals (AM-177)

Jean-Michel Bismut

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691151298
eISBN:
9781400840571
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691151298.001.0001
Subject:
Mathematics, Geometry / Topology

This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators ... More


Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)

Christopher D. Sogge

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691160757
eISBN:
9781400850549
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691160757.001.0001
Subject:
Mathematics, Numerical Analysis

Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. The book gives a proof of the sharp Weyl ... More


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