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During the last part of the editorial processing of this article, our dear friend and colleague Luis Sánchez-González passed away unexpectedly. We dedicate this paper to his memory.Abstract. The concept of subdifferentiability is studied in the context of C 1 Finsler manifolds (modeled on a Banach space with a Lipschitz C 1 bump function). A class of Hamilton-Jacobi equations defined on C 1 Finsler manifolds is studied and several results related to the existence and uniqueness of viscosity solutions are obtained.

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