Horizontal Gauss Curvature Flow of Graphs in Carnot Groups

2009/02/10 by Erin Martin, Erin Haller Martin, Martin, Erin Haller
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.0902.1760

arxiv created 2009/02/10 · openalex publication_date 2009/02/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show the existence of continuous viscosity solutions to the equation describing the flow of a graph in the Carnot group G x R according to its horizontal Gauss curvature. In doing so, we prove a comparison principle for degenerate parabolic equations of the form u_t + F(D₀u, (D₀²u)^*) = 0 for u defined on G.

Citations

• Constant mean curvature surfaces in sub-Riemannian geometry

Related

• Generalized mean curvature flow in Carnot groups
• Sub-Riemannian heat kernels and mean curvature flow of graphs
• Anisotropic Gauss curvature flow of complete non-compact graphs
• Comparison Principles for subelliptic equations of Monge-Ampere type
• The Parabolic Infinite-Laplace Equation in Carnot groups