In this paper, we study the existence and multiplicity problems for orthogonal Finsler geodesic chords in a manifold with boundary which is homeomorphic to a $ N $-dimensional disk. Under a suitable assumption, which is weaker than convexity, we prove that, if the Finsler metric is reversible, then there are at least $ N $ orthogonal Finsler geodesic chords that are geometrically distinct. If the reversibility assumption does not hold, then there are at least two orthogonal Finsler geodesic chords with different values of the energy functional.

中文翻译：

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Finsler 圆盘中正交测地线的重数结果

在本文中，我们研究了具有同胚于$N$维圆盘边界的流形中正交Finsler测地线的存在性和多重性问题。在一个弱于凸性的合适假设下，我们证明，如果 Finsler 度量是可逆的，那么至少有 $N$ 个正交的 Finsler 测地线在几何上是不同的。如果可逆性假设不成立，则至少有两个具有不同能量泛函值的正交芬斯勒测地线。