
Journal of Convex Analysis 20 (2013), No. 1, 067091 Copyright Heldermann Verlag 2013 Euler Characteristic of EpiLipschitz Subsets of Riemannian Manifolds S. Hosseini Dept. of Mathematics, University of Isfahan, P. O. Box 81745163, Isfahan, Iran hoseini@math.ui.ac.ir Mohamad Reza Pouryayevali Dept. of Mathematics, University of Isfahan, P. O. Box 81745163, Isfahan, Iran pourya@math.ui.ac.ir We present some properties of tangent and normal cones of epiLipschitz subsets of complete Riemannian manifolds. The fact that epiLipschitz subsets of complete Riemannian manifolds are absolute neighborhood retracts is proved. A notion of Euler characteristic of epiLipschitz subsets of complete Riemannian manifolds is introduced. Moreover, we provide a sufficient condition which ensures that the Euler characteristic of this class of sets is equal to one. Then, these results are applied to equilibrium theory on complete parallelizable Riemannian manifolds. Keywords: Clarke subdifferential, EpiLipschitz sets, Euler characteristic, Riemannian manifolds. MSC: 49J52, 58E05, 58C30, 55M25 [ Fulltextpdf (216 KB)] for subscribers only. 