#### Vol. 317, No. 2, 2022

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Smooth solutions to the Gauss image problem

### Li Chen, Di Wu and Ni Xiang

Vol. 317 (2022), No. 2, 275–295
##### Abstract

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.

##### Keywords
Monge–Ampère equation, the Gauss image problem, Gauss curvature flow, existence of solutions
##### Mathematical Subject Classification 2010
Primary: 35J96
Secondary: 52A20, 53C44