A Morse type uniqueness theorem for non-parametric minimizing hypersurfaces

2007/07/02 by Hannes Junginger-Gestrich, Junginger-Gestrich, Hannes
Mathematics · #35J20 #37C85 #58E30 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #math.AP #math.DS #msc:35J20 #msc:37C85 #msc:58E30

paper · pdf · doi:10.48550/arxiv.0707.0017

17 pages, 1 figure

arxiv created 2007/07/02 · arxiv updated 2009/12/01

Abstract

A classical result about minimal geodesics on R² with Z² periodic metric that goes back to H.M. Morse asserts that a minimal geodesic that is asymptotic to a periodic minimal geodesic cannot intersect any periodic minimal geodesic of the same period. This paper treats a similar theorem for nonparametric minimizing hypersurfaces without selfintersections -- as were studied by J. Moser, V. Bangert, P.H. Rabinowitz, E. Stredulinsky and others.

Related

• Existence of infinitely many minimal hypersurfaces in low dimensions, after F.C. Marques, A.A. Neves et A. Song (Bourbaki Seminar)
• Minimal rays on surfaces of genus greater than one
• On a remarkable example of F. Almgren and H. Federer in the global theory of minimizing geodesics
• Riemannian metrics on the sphere with Zoll families of minimal hypersurfaces
• Metrics without Morse index bounds