caa a22 4500 445843489 CHVBK 20180317145351.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s00526-010-0343-1 doi (NATIONALLICENCE)springer-10.1007/s00526-010-0343-1 Convex domains of Finsler and Riemannian manifolds [Elektronische Daten] [Rossella Bartolo, Erasmo Caponio, Anna Germinario, Miguel Sánchez] A detailed study of the notions of convexity for a hypersurface in a Finsler manifold is carried out. In particular, the infinitesimal and local notions of convexity are shown to be equivalent. Our approach differs from Bishop's one in his classical result (Bishop, Indiana Univ Math J 24:169-172, 1974) for the Riemannian case. Ours not only can be extended to the Finsler setting but it also reduces the typical requirements of differentiability for the metric and it yields consequences on the multiplicity of connecting geodesics in the convex domain defined by the hypersurface. Springer-Verlag, 2010 Bartolo Rossella Dipartimento di Matematica, Politecnico di Bari, Via Orabona 4, 70125, Bari, Italy aut Caponio Erasmo Dipartimento di Matematica, Politecnico di Bari, Via Orabona 4, 70125, Bari, Italy aut Germinario Anna Dipartimento di Matematica, Università degli Studi di Bari, Via Orabona 4, 70125, Bari, Italy aut Sánchez Miguel Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, Campus Fuentenueva s/n, 18071, Granada, Spain aut Calculus of Variations and Partial Differential Equations Springer-Verlag 40/3-4(2011-03-01), 335-356 0944-2669 40:3-4<335 2011 40 526 https://doi.org/10.1007/s00526-010-0343-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00526-010-0343-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bartolo Rossella Dipartimento di Matematica, Politecnico di Bari, Via Orabona 4, 70125, Bari, Italy aut NATIONALLICENCE 700 1- Caponio Erasmo Dipartimento di Matematica, Politecnico di Bari, Via Orabona 4, 70125, Bari, Italy aut NATIONALLICENCE 700 1- Germinario Anna Dipartimento di Matematica, Università degli Studi di Bari, Via Orabona 4, 70125, Bari, Italy aut NATIONALLICENCE 700 1- Sánchez Miguel Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, Campus Fuentenueva s/n, 18071, Granada, Spain aut NATIONALLICENCE 773 0- Calculus of Variations and Partial Differential Equations Springer-Verlag 40/3-4(2011-03-01), 335-356 0944-2669 40:3-4<335 2011 40 526 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer