Tubes
著者
書誌事項
Tubes
（Progress in mathematics, v. 221）
Birkhäuser Verlag, c2004
2nd ed
- : Basel
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注記
Includes bibliographical references (p. [257]-271) and indexes
内容説明・目次
内容説明
This book expresses the full understanding of Weyl's formula for the volume of a tube, its roots and its implications. Historical notes and Mathematica drawings have been added to this revised second edition.
From the reviews:
"Will do much to make Weyl's tube formula more accessible to modern readers.... A high point is the presentation of estimates for the volumes of tubes in ambient Riemannian manifolds whose curvature is bounded above or below."
--BULLETIN OF THE AMS
目次
1 An Introduction to Weyl's Tube Formula.- 3 The Riccati Equation for Second Fundamental Forms.- 4 The Proof of Weyl's Tube Formula.- 5 The Generalized Gauss-Bonnet Theorem.- 6 Chern Forms and Chern Numbers.- 7 The Tube Formula in the Complex Case.- 8 Comparison Theorems for Tube Volumes.- 9 Power Series Expansions for Tube Volumes.- 10 Steiner's Formula.- 11 Mean-value Theorems.- Appendix A.- A.2 Moments.- A.3 Computation of the Volume of a Geodesic Ball.- Appendix B.- Notation Index.- Name Index.
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