On subdifferential in Hadamard spaces

Abstract

In this paper, we deal with the subdifferential concept on Hadamard spaces. Flat Hadamard spaces are characterized, and necessary and suficient conditions are presented to prove that the subdifferential set in Hadamard spaces is nonempty. Proximal subdifferential in Hadamard spaces is addressed and some basic properties are high-lighted. Finally, a density theorem for subdifferential set is established.