A unified flow approach to smooth L^p Christoffel-Minkowski problem for p>1

2023/01/16 by Zhang, Ruijia
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2301.06491

Abstract

In this paper we study an anisotropic expanding flow of smooth, closed, uniformly convex hypersurfaces in ℝⁿ⁺¹ with speed ψσ_k(λ)^α, where α is a positive constant, σ_k(λ) is the k-th elementary symmetric polynomial of the principal radii of curvature and ψ is a preassigned positive smooth function defined on \mathbbSⁿ. We prove that under some assumptions of ψ, the solution to the flow after normalisation exists for all time and converges smoothly to a solution of the well-known L^p Christoffel-Minkowski problem u^1-p( x ) σ_k ( ∇²u+uI)=cψ(x) for p>1.

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