Equilibria on $L$-retracts in Riemannian manifolds

Seyedehsomayeh Hosseini, Mohamad R. Pouryayevali

DOI: http://dx.doi.org/10.12775/TMNA.2016.017


We introduce a class of subsets of Riemannian manifolds called the $L$-retract. Next we consider a topological degree for set-valued upper semicontinuous maps defined on open sets of compact $L$-retracts in Riemannian manifolds. Then, we present a theorem on the existence of equilibria (or zeros) of an upper semicontinuous set-valued map with nonempty closed convex values satisfying the tangency condition defined on a compact $L$-retract in a Riemannian manifold.


Set-valued map; degree theory; Euler characteristic; equilibrium

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