A logarithmic Gauss curvature flow and the Minkowski problem

Abstract

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On the Orlicz Minkowski Problem for Polytopes

“…Although the solution of the Minkowski problem has been known in the mathematical literature since the work of Minkowski [44,45], Alexandrov [1][2][3], Fenchel and Jessen [10], analytic versions or algorithmic issues of the problem are still subject of current research and highly relevant (see, e.g., Chou and Wang [7], Jerison [21], Klain [23], Lamberg [24], Lamberg and Kaasalainen [25], and the reference therein).…”

Surfaces expanding by the inverse Gauß curvature flow

“…This was extended in [16,25]. There are also inhomogeneous flows for which solutions converge to round spheres as t ↑ ∞ [6,9,10,18].…”

Forced convex mean curvature flow in Euclidean spaces

“…If the ambient space is a Minkowski space, Aarons [1] studied the forced mean curvature flow of graphs and obtained the long time existence and convergence under suitable assumptions on h(t). And a kind of trichotomy to the initial hypersurface was used by Chou-Wang [4] in logarithmic Gauss curvature flow. This paper is organized as follows: Section 2 introduces some known results on curvature flow (1.1) and some preliminary facts of convex hypersurfaces, which will be used later.…”