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| SoftcoverISBN: | 978-1-4704-4185-2 |
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| Softcover ISBN: | 978-1-4704-4185-2 |
| Product Code: | MEMO/265/1290 |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| eBook ISBN: | 978-1-4704-6148-5 |
| Product Code: | MEMO/265/1290.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Softcover ISBN: | 978-1-4704-4185-2 |
| eBookISBN: | 978-1-4704-6148-5 |
| Product Code: | MEMO/265/1290.B |
| List Price: | $170.00$127.50 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 265; 2020; 62 ppMSC: Primary 58;
The authors develop a degree theory for compact immersed hypersurfaces of prescribed \(K\)-curvature immersed in a compact, orientable Riemannian manifold, where \(K\) is any elliptic curvature function. They apply this theory to count the (algebraic) number of immersed hyperspheres in various cases: where \(K\) is mean curvature, extrinsic curvature and special Lagrangian curvature and show that in all these cases, this number is equal to \(-\chi(M)\), where \(\chi(M)\) is the Euler characteristic of the ambient manifold \(M\).
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Table of Contents
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Chapters
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1. Introduction
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2. Degree theory
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3. Applications
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A. Weakly smooth maps
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B. Prime immersions
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Additional Material
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RequestsReview Copy – for reviewers who would like to review an AMS bookPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
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The authors develop a degree theory for compact immersed hypersurfaces of prescribed \(K\)-curvature immersed in a compact, orientable Riemannian manifold, where \(K\) is any elliptic curvature function. They apply this theory to count the (algebraic) number of immersed hyperspheres in various cases: where \(K\) is mean curvature, extrinsic curvature and special Lagrangian curvature and show that in all these cases, this number is equal to \(-\chi(M)\), where \(\chi(M)\) is the Euler characteristic of the ambient manifold \(M\).
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Chapters
-
1. Introduction
-
2. Degree theory
-
3. Applications
-
A. Weakly smooth maps
-
B. Prime immersions
