Journal of Convex Analysis 20 (2013), No. 1, 067--091
Copyright Heldermann Verlag 2013
Euler Characteristic of Epi-Lipschitz Subsets of Riemannian Manifolds
S. Hosseini
Dept. of Mathematics, University of Isfahan, P. O. Box 81745-163, Isfahan, Iran
hoseini@math.ui.ac.ir
Mohamad Reza Pouryayevali
Dept. of Mathematics, University of Isfahan, P. O. Box 81745-163, Isfahan, Iran
pourya@math.ui.ac.ir
We present some properties of tangent and normal cones of epi-Lipschitz subsets of complete Riemannian manifolds. The fact that epi-Lipschitz subsets of complete Riemannian manifolds are absolute neighborhood retracts is proved. A notion of Euler characteristic of epi-Lipschitz 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, Epi-Lipschitz sets, Euler characteristic, Riemannian manifolds.
MSC: 49J52, 58E05, 58C30, 55M25
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