Linklist Manifolds with Corners
In this post I am (continuously) collecting a couple of links to books, papers, talks etc. surrounding topics connected with manifolds with corners and in particular differential operators on them.
The selections is obviously due to my personal interests and taste and I do not claim that the list has all "important" material listed.
Currently (WS22/23-SS23), we are working through Melrose's unfinished book in our Oberseminar.
In order to understand the material, I am preparing somewhat updated notes based on Melrose and the material presented here. In the end I might also publish those notes in the hope that they may help other people start their journey through singular analysis more easily.
Introductory material
- Grieser - Basics of the b-calculus arXiv:math/0010314
- Grieser - Scales, blow-up and quasimode constructions arXiv:1607.04171
- Grieser - Polyhomogeneous functions, regularized
integrals, push-forward theorem etc.
Books
- Melrose - Differential analysis on manifolds with corners. This is a book in preparation and is partially available at Melrose's webpage
- Melrose - The Atiyah-Patodi-Singer Index Theorem. This book contains many detailed discussions concerning the b-calculus. (Web, MAthSciNet)
Video lectures
- Melrose (and others) @MSRI Introductory Workshop on Analysis on Singular Spaces
- Melrose Real Blow-ups, Lecture notes. (2008)
- Melrose @GlobalPoissonWebinar Resolution of Lie algebroids and quantization
Articles
- The definition of manifolds with corners. Although manifolds with corners appear rather naturally as products of manifolds with boundary, there is no universal notion that all people agree upon when they talk about a manifold with corners.
- Joyce, 2010: On manifolds with corners (arXiv, MathSciNet)
- Joyce, 2016: Manifolds with analytic corners (arXiv)
- Joyce, 2016: A generalization of manifolds with corners (arXiv, MathSciNet, DOI)
- Differential forms on manifolds with corners
- Gürer, Iglesias-Zemmour, 2019: Differential forms on manifolds with boundary and cornners (MathSciNet, DOI)
- Blow-ups on manifolds with corners
- Melrose, 2008: Real Blow-ups, Lecture notes
- Kottke, 2018: Blow-ups in manifolds with genralized corners (arXiv, MathSciNet, DOI)
