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2 results

Anisotropic Gauss curvature flows and their associated Dual Orlicz-Minkowski problems
Part of
- Elliptic equations and systems
- Global differential geometry
Li Chen, Qiang Tu, Di Wu, Ni Xiang
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 152 / Issue 1 / February 2022

Published online by Cambridge University Press:

01 November 2021, pp. 148-162

Print publication:

February 2022
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In this paper we study a normalized anisotropic Gauss curvature flow of strictly convex, closed hypersurfaces in the Euclidean space. We prove that the flow exists for all time and converges smoothly to the unique, strictly convex solution of a Monge-Ampère type equation and we obtain a new existence result of solutions to the Dual Orlicz-Minkowski problem for smooth measures, especially for even smooth measures.

A two-dimensional random crystalline algorithm for Gauss curvature flow
Part of
- Markov processes
- Geometric probability and stochastic geometry
H. Ishii, T. Mikami
Journal:

Advances in Applied Probability / Volume 34 / Issue 3 / September 2002

Published online by Cambridge University Press:

01 July 2016, pp. 491-504

Print publication:

September 2002
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We propose and study a random crystalline algorithm (a discrete approximation) of the Gauss curvature flow of smooth simple closed convex curves in ℝ2 as a stepping stone to the full understanding of such phenomena as the wearing process of stones on a beach.

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2 results

Anisotropic Gauss curvature flows and their associated Dual Orlicz-Minkowski problems

A two-dimensional random crystalline algorithm for Gauss curvature flow