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Smooth solutions to
the Gauss image problem
Li Chen, Di Wu and Ni Xiang |
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Vol. 317 (2022), No. 2, 275–295
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Abstract |
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We study the Gauss image problem, a generalization of the Aleksandrov problem in convex geometry. By considering a geometric flow involving Gauss curvature and functions of normal vectors and radial vectors, we obtain the existence of smooth solutions to this problem. |
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Keywords
Monge–Ampère equation, the Gauss image problem, Gauss
curvature flow, existence of solutions
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Mathematical Subject Classification 2010
Primary: 35J96
Secondary: 52A20, 53C44
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Milestones
Received: 9 August 2021
Revised: 25 January 2022
Accepted: 19 February 2022
Published: 14 July 2022
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Authors |
| Li Chen | |
| Faculty of Mathematics and
Statistics Hubei Key Laboratory of Applied Mathematics HuBei University WuHan China |
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| Di Wu | |
| Faculty of Mathematics and
Statistics Hubei Key Laboratory of Applied Mathematics HuBei University WuHan China |
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| Ni Xiang | |
| Faculty of Mathematics and
Statistics Hubei Key Laboratory of Applied Mathematics HuBei University WuHan China |
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