arXiv 1503.061762015-03-20math.DS

Functions on the sphere with critical points in pairs and orthogonal geodesic chords

R. Giambò, F. Giannoni, P. Piccione

备注：: 12 pages, 3 figures

英文摘要：

Using an estimate on the number of critical points for a Morse-even function on the sphere $\mathbb S^m$, $m\ge1$, we prove a multiplicity result for orthogonal geodesic chords in Riemannian manifolds with boundary that are diffeomorphic to Euclidean balls. This yields also a multiplicity result for brake orbits in a potential well.

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