David Xianfeng Gu, Emil Saucan

Classical and Discrete Differential Geometry (eBook, PDF)

Theory, Applications and Algorithms

• Format: PDF

Produktbeschreibung

This book introduces differential geometry and cutting-edge findings from the discipline by incorporating both classical approaches and modern discrete differential geometry across all facets and applications, including graphics and imaging, physics and networks.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 588
• Erscheinungstermin: 31. Januar 2023
• Englisch
• ISBN-13: 9781000804454
• Artikelnr.: 67286977

Autorenporträt

David Xianfeng Gu is a SUNY Empire Innovation Professor of Computer Science and Applied Mathematics at State University of New York at Stony Brook, USA. His research interests focus on generalizing modern geometry theories to discrete settings and applying them in engineering and medical fields and recently on geometric views of optimal transportation theory. He is one of the major founders of an interdisciplinary field, Computational Conformal Geometry.

Emil Saucan is Associate Professor of Applied Mathematics at Braude College of Engineering, Israel. His main research interest is geometry in general (including Geometric Topology), especially Discrete and Metric Differential Geometry and their applications to Imaging and Geometric Design, as well as Geometric Modeling. His recent research focuses on various notions of discrete Ricci curvature and their practical applications.

Inhaltsangabe

Section I Differential Geometry, Classical and Discrete 1. Curves 2.
Surfaces: Gauss Curvature - First Definition 3. Metrization of Gauss
Curvature 4. Gauss Curvature and Theorema Egregium 5. The Mean and Gauss
Curvature Flows 6. Geodesics 7. Geodesics and Curvature 8. The Equations of
Compatibility 9. The Gauss-Bonnet Theorem and the Poincare Index Theorem
10. Higher Dimensional Curvatures 11. Higher Dimensional Curvatures 12.
Discrete Ricci Curvature and Flow 13. Weighted Manifolds and Ricci
Curvature Revisited Section II Differential Geometry, Computational Aspects
14. Algebraic Topology 15. Homology and Cohomology Group 16. Exterior
Calculus and Hodge Decomposition 17. Harmonic Map 18. Riemann Surface 19.
Conformal Mapping 20. Discrete Surface Curvature Flows 21. Mesh Generation
Based on Abel-Jacobi Theorem Section III Appendices 22. Appendix A 23.
Appendix B 24. Appendix C