An application of dual convex bodies to the inverse Gauss curvature flow

2013/12/16 by Mohammad N. Ivaki, Ivaki, Mohammad N.
Mathematics · #52A05 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #Primary 53C44 #Secondary 35K55 #math.DG #msc:35K55 #msc:52A05 #msc:53C44

paper · pdf · doi:10.48550/arxiv.1312.4242

To appear in Proc. Amer. Math. Soc

openalex publication_date 2013/12/16 · arxiv created 2014/02/25 · arxiv updated 2014/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By means of dual convex bodies, we obtain regularity of solutions to the expanding Gauss curvature flows with homogeneity degrees -p, 0<p<1. At the end, we remark that our method can also be used to obtain regularity of solutions to the shrinking Gauss curvature flows with homogeneity degrees less than one.

Citations

• Surfaces moving by powers of Gauss curvature
• Contracting convex hypersurfaces by curvature

Related

• A note on the Gauss curvature flow
• Inverse Gauss curvature flows with free boundaries in a cone
• Surfaces expanding by the inverse Gauss curvature flow
• Flow by Gauss curvature to Dual Orlicz-Minkowski problems
• Flow by the power of the Gauss curvature