A Simple Formula for Scalar Curvature of Level Sets in Euclidean Spaces

2013/01/10 by Yajun Zhou, Zhou, Yajun · 1 citation
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Point processes and geometric inequalities #math-ph #math.AP #math.DG #math.MP

paper · pdf · doi:10.48550/arxiv.1301.2202

15 pages

arxiv created 2013/01/10 · openalex publication_date 2013/01/10 · arxiv updated 2013/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A simple formula is derived for the Ricci scalar curvature of any smooth level set ψ(x₀,x₁,...,x_n)=C embedded in the Euclidean space \mathbb Rⁿ⁺¹, in terms of the gradient ∇ψ and the Laplacian Δψ. Some applications are given to the geometry of low-dimensional p-harmonic functions and high-dimensional harmonic functions.

Citations

• Classical Electrodynamics

Cited by

• Geometric Entanglement Entropy on Projective Hilbert Space

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