Existence of variationally defined curves in complete Riemannian manifolds

2013/12/19 by Philip Schrader, Schrader, Philip
Engineering · Mathematics · #3D Shape Modeling and Analysis #49J05 #58E25 #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1312.5414

openalex publication_date 2013/12/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We present a method for proving the existence of solutions to a class of one dimensional variational problems. The method is demonstrated by two examples of optimal interpolation problems which are motivated by engineering applications. In each case we prove that the variational problem satisfies the Palais-Smale condition and the existence of a minimal solution and lower bounds for the number of stationary curves then follow.

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