Aspects of Differential Geometry V

Erscheinungsjahr 2021
ISBN: 978-1-63639-112-0
Verlag: Morgan & Claypool Publishers

Buch, Englisch, 156 Seiten, Hardback, Format (B × H): 191 mm x 235 mm

Reihe: Synthesis Lectures on Mathematics and Statistics

Book V completes the discussion of the first four books by treating in some detail the analytic results in elliptic operator theory used previously. Chapters 16 and 17 provide a treatment of the techniques in Hilbert space, the Fourier transform, and elliptic operator theory necessary to establish the spectral decomposition theorem of a self-adjoint operator of Laplace type and to prove the Hodge Decomposition Theorem that was stated without proof in Book II. In Chapter 18, we treat the de Rham complex and the Dolbeault complex, and discuss spinors. In Chapter 19, we discuss complex geometry and establish the Kodaira Embedding Theorem.

Autoren/Hrsg.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

- Preface
- Acknowledgments
- Functional Analysis
- Elliptic Operator Theory
- Potential Theory
- Complex Geometry
- Bibliography
- Authors' Biographies
- Index