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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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