The method of moving planes: a quantitative approach

2018/11/13 by Giulio Ciraolo, Ciraolo, Giulio, Alberto Roncoroni +1 · 2 citations
Engineering · #Analysis of PDEs (math.AP) #Architecture and Computational Design #BIM and Construction Integration #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1811.05202

openalex publication_date 2018/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We review classical results where the method of the moving planes has been used to prove symmetry properties for overdetermined PDE's boundary value problems (such as Serrin's overdetermined problem) and for rigidity problems in geometric analysis (like Alexandrov soap bubble Theorem), and we give an overview of some recent results related to quantitative studies of the method of moving planes, where quantitative approximate symmetry results are obtained.

Cited by

• Convergence to Radial Symmetry in Iterative Convolution-Thresholding Dynamics
• Hessian operators, overdetermined problems, and higher order mean curvatures: symmetry and stability results

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