Selected Applications Of Geometry To Low Dimensional Topology
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Selected Applications of Geometry to Low-Dimensional Topology
Author: Michael H. Freedman
language: en
Publisher: American Mathematical Soc.
Release Date: 1990
Based on lectures presented at Pennsylvania State University in February 1987, this work begins with the notions of manifold and smooth structures and the Gauss-Bonnet theorem, and proceeds to the topology and geometry of foliated 3-manifolds. It also explains why four-dimensional space has special attributes.
Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics
Author: Josi A. de Azcárraga
language: en
Publisher: Cambridge University Press
Release Date: 1998-08-06
A self-contained introduction to the cohomology theory of Lie groups and some of its applications in physics.
Harmonic Measure
Recent developments in geometric measure theory and harmonic analysis have led to new and deep results concerning the regularity of the support of measures which behave "asymptotically" (for balls of small radius) as the Euclidean volume. A striking feature of these results is that they actually characterize flatness of the support in terms of the asymptotic behavior of the measure. Such characterizations have led to important new progress in the study of harmonic measure fornon-smooth domains. This volume provides an up-to-date overview and an introduction to the research literature in this area. The presentation follows a series of five lectures given by Carlos Kenig at the 2000 Arkansas Spring Lecture Series. The original lectures have been expanded and updated to reflectthe rapid progress in this field. A chapter on the planar case has been added to provide a historical perspective. Additional background has been included to make the material accessible to advanced graduate students and researchers in harmonic analysis and geometric measure theory.