**
Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 26, No. 2, pp. 209-219 (2010)
**

#
Geodesics on non-complete Finsler manifolds

##
Rossella Bartolo

Politecnico di Bari

**Abstract:** In this note we deal with domains $D$ (i.e. connected open subsets) of a Finsler manifold $(M,F)$. At first we carry out a comparison between different notions of convexity for their boundaries. Then a careful application of variational methods to the geodesic problem yields that the convexity of $\partial D$ is equivalent to the existence of a minimal geodesic for each pair of points of $D$. Furthermore multiplicity of connecting geodesics can be obtained if $D$ is not contractible.

**Keywords:** Finsler manifold, minimizing geodesic, convex boundary, penalization technique

**Classification (MSC2000):** 53C60; 58B20, 53C22

**Full text of the article:**

[Previous Article] [Next Article] [Contents of this Number]

*
© 2010–2011
FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition
*