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Degree Theory of Immersed Hypersurfaces
 
Harold Rosenberg IMPA, Rio de Janeiro, Brazil
Graham Smith Centre de Recerca Matematica, Barcelona, Spain
Degree Theory of Immersed Hypersurfaces
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
eBook: ISBN:  978-1-4704-6148-5
Product Code:  MEMO/265/1290.B
List Price: $170.00 $127.50
MAA Member Price: $153.00 $114.75
AMS Member Price: $136.00 $102.00
Degree Theory of Immersed Hypersurfaces
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Degree Theory of Immersed Hypersurfaces
Harold Rosenberg IMPA, Rio de Janeiro, Brazil
Graham Smith Centre de Recerca Matematica, Barcelona, Spain
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
eBook ISBN:  978-1-4704-6148-5
Product Code:  MEMO/265/1290.B
List Price: $170.00 $127.50
MAA Member Price: $153.00 $114.75
AMS Member Price: $136.00 $102.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2652020; 62 pp
    MSC: 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 \(M\).

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Degree theory
    • 3. Applications
    • A. Weakly smooth maps
    • B. Prime immersions
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2652020; 62 pp
MSC: 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 \(M\).

  • Chapters
  • 1. Introduction
  • 2. Degree theory
  • 3. Applications
  • A. Weakly smooth maps
  • B. Prime immersions
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.