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

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• 作者：Roberto Giambò ; ^a ; ^{roberto.giambo@unicam.it" class="auth_mail" title="E-mail the corresponding author} ; Fabio Giannoni^a ; ^{fabio.giannoni@unicam.it" class="auth_mail" title="E-mail the corresponding author} ; Paolo Piccione^b ; ^{piccione.p@gmail.com" class="auth_mail" title="E-mail the corresponding author} ;
• 关键词：58E05 ; 58E10 ; 53C22
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：5 June 2016
• 年：2016
• 卷：260
• 期：11
• 页码：8261-8275
• 全文大小：329 K

文摘

Using an estimate on the number of critical points for a Morse-even   function on the sphere 18ea60004f61f2cf8875de8038" title="Click to view the MathML source">S^m${\mathbb{S}}^m$, m≥1$m\ge 1$, 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.