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Softcover ISBN: | 978-1-4704-3524-0 |
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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 |
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Softcover ISBN: | 978-1-4704-3524-0 |
eBook ISBN: | 978-1-4704-5243-8 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 259; 2019; 83 ppMSC: 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.
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Table of Contents
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Chapters
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1. Introduction
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2. Basic definitions and the Constant Rank Theorem technique
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3. A microscopic space-time Convexity Principle for space-time level sets
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4. The Strict Convexity of Space-time Level Sets
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5. Appendix: the proof in dimension $n=2$
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Additional Material
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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.
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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 $n=2$