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On Space-Time Quasiconcave Solutions of the Heat Equation
 
Chuanqiang Chen Zhejiang University of Technology, Hangzhou, China
Xinan Ma University of Science and Technology of China, Hefei, China
Paolo Salani Università di Firenze, Firenze, Italy
On Space-Time Quasiconcave Solutions of the Heat Equation
Softcover ISBN:  978-1-4704-3524-0
Product Code:  MEMO/259/1244
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
eBook ISBN:  978-1-4704-5243-8
Product Code:  MEMO/259/1244.E
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
Softcover ISBN:  978-1-4704-3524-0
eBook: ISBN:  978-1-4704-5243-8
Product Code:  MEMO/259/1244.B
List Price: $162.00 $121.50
MAA Member Price: $145.80 $109.35
AMS Member Price: $97.20 $72.90
On Space-Time Quasiconcave Solutions of the Heat Equation
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On Space-Time Quasiconcave Solutions of the Heat Equation
Chuanqiang Chen Zhejiang University of Technology, Hangzhou, China
Xinan Ma University of Science and Technology of China, Hefei, China
Paolo Salani Università di Firenze, Firenze, Italy
Softcover ISBN:  978-1-4704-3524-0
Product Code:  MEMO/259/1244
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
eBook ISBN:  978-1-4704-5243-8
Product Code:  MEMO/259/1244.E
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
Softcover ISBN:  978-1-4704-3524-0
eBook ISBN:  978-1-4704-5243-8
Product Code:  MEMO/259/1244.B
List Price: $162.00 $121.50
MAA Member Price: $145.80 $109.35
AMS Member Price: $97.20 $72.90
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2592019; 83 pp
    MSC: Primary 35

    In this paper the authors first obtain a constant rank theorem for the second fundamental form of the space-time level sets of a space-time quasiconcave solution of the heat equation. Utilizing this constant rank theorem, they obtain some strictly convexity results of the spatial and space-time level sets of the space-time quasiconcave solution of the heat equation in a convex ring. To explain their ideas and for completeness, the authors also review the constant rank theorem technique for the space-time Hessian of space-time convex solution of heat equation and for the second fundamental form of the convex level sets for harmonic function.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Basic definitions and the Constant Rank Theorem technique
    • 3. A microscopic space-time Convexity Principle for space-time level sets
    • 4. The Strict Convexity of Space-time Level Sets
    • 5. Appendix: the proof in dimension $n=2$
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
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Volume: 2592019; 83 pp
MSC: Primary 35

In this paper the authors first obtain a constant rank theorem for the second fundamental form of the space-time level sets of a space-time quasiconcave solution of the heat equation. Utilizing this constant rank theorem, they obtain some strictly convexity results of the spatial and space-time level sets of the space-time quasiconcave solution of the heat equation in a convex ring. To explain their ideas and for completeness, the authors also review the constant rank theorem technique for the space-time Hessian of space-time convex solution of heat equation and for the second fundamental form of the convex level sets for harmonic function.

  • Chapters
  • 1. Introduction
  • 2. Basic definitions and the Constant Rank Theorem technique
  • 3. A microscopic space-time Convexity Principle for space-time level sets
  • 4. The Strict Convexity of Space-time Level Sets
  • 5. Appendix: the proof in dimension $n=2$
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
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