Green Function Rigidity for Two Dimensional Sphere

2026/01/07 by Mijia Lai, Chilin Zhang
Mathematics · #Conjecture #Differential geometry #Euclidean geometry #Fourier analysis #Geometric Analysis and Curvature Flows #Green's function for the three-variable Laplace equation #Nonlinear Partial Differential Equations #Point processes and geometric inequalities #Rigidity (electromagnetism) #Surface (topology) #Unit sphere #math.AP #math.DG

paper · pdf · doi:10.1007/s12220-026-02549-z

published in Journal of Geometric Analysis 36(8) (Springer Science+Business Media)

openalex publication_date 2026/07/21 · openalex created_date 2026/07/22 · openalex updated_date 2026/07/28

Abstract

We verify a conjecture proposed by X. Chen and Y. Shi, which arises from their study of the Green function on spheres in Euclidean space. More precisely, let M⊂ ℝ³ be a closed C² embedded surface and suppose that there exists a point p∈ M so that its Green function G is of the form G(p,q)=-(1)/(2π) ln d_ℝ³(p,q)+c, ∀ q≠ p, then M must be a round sphere.

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