2008/11/29 by Victor Alexandrov, Victor A. Alexandrov · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Point processes and geometric inequalities #math.DG #math.MG #msc:52C25 #msc:53C42 #msc:53C45
paper · pdf · doi:10.1007/s11202-009-0087-3
published as Siberian Math. J. 50, no. 5 (2009), 757-759 · 4 pages
arxiv created 2008/11/29 · openalex publication_date 2009/09/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
Using Green's theorem we reduce the variation of the total mean curvature of a smooth surface in the Euclidean 3-space to a line integral of a special vector field and obtain the following well-known theorem as an immediate consequence: the total mean curvature of a closed smooth surface in the Euclidean 3-space is stationary under an infinitesimal flex.